diff --git a/CHANGELOG.md b/CHANGELOG.md
index 2c2142bc..72e60cf8 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -9,6 +9,7 @@
 - `issue query --state` and `issue mine --state` accept a workflow state name or ID as well as the six state types, looked up within the queried team scope (all teams under `--all-teams`, where a name matches every team's same-named state). An unknown name errors and lists the scope's states, and types and names can be mixed
 - `project update --content <markdown>` and `--content-file <path>` replace a project's long-form overview body, matching the flags `project create` already had. Previously the only way to change the body after creation was a hand-written `projectUpdate` mutation through `linear api`
 - `issue update --clear-due-date`, `--clear-estimate`, `--clear-parent`, `--clear-project`, and `--clear-milestone`, plus `project update --clear-lead`, `--clear-start-date`, and `--clear-target-date`, to remove a value the way `--unassign` and `--clear-cycle` already do. Each sends an explicit `null` to Linear and errors when combined with its set flag; `--clear-project` also rejects `--milestone`, since a milestone belongs to the project being removed. Previously these fields could only be changed, never cleared: cliffy treats `--due-date ""` as a missing value
+- `project update` now changes teams, labels, and initiatives with the same three operations `issue update` has for labels: `--team`, `--label`, and `--initiative` replace the whole set, `--add-team`/`--add-label`/`--add-initiative` append, and `--remove-team`/`--remove-label`/`--remove-initiative` detach, all repeatable, with a replace flag rejected alongside its add/remove flags. Linear's project input only accepts a full `teamIds`/`labelIds` list, so add and remove read the project's current set (every page of it) and send the computed set; initiatives have no input field at all and go through the initiative-to-project link mutations, so `project update` previously could not change them after `project create --initiative`. Removing a team, label, or initiative the project does not have errors and lists what it does have, and a link change that fails part-way reports what was applied and what is still pending
 - `--json` (`-j`) on `team list`, `cycle list`, `cycle view`, `milestone list`, `milestone view`, and `project view`, the last read commands without machine-readable output. List commands emit the same `{ nodes, pageInfo }` connection shape as the other list commands, after the same filtering and ordering as the table; view commands emit the GraphQL object as fetched, including every issue rather than the ten-item preview, and `milestone view --all --json` includes every page. (A 2.0.0 entry claimed `cycle list --json`; that change never actually landed.) ([#276](https://github.com/schpet/linear-cli/issues/276); thanks @lakardion)
 
 ### Fixed
diff --git a/README.md b/README.md
index 6e62c1f0..e9c4e328 100644
--- a/README.md
+++ b/README.md
@@ -204,6 +204,8 @@ linear project create --name "API v2" --team ENG --content-file overview.md
 linear project create --name "Mobile launch" --team APP --priority high --label Launch --member jane@example.com
 linear project update <projectId> --content-file overview.md  # replace the project's overview body
 linear project update <projectId> --clear-lead --clear-target-date  # remove values (also --clear-start-date)
+linear project update <projectId> --add-team OPS --remove-label Launch --add-initiative "Q4 Bets"  # change teams, labels, initiatives incrementally
+linear project update <projectId> --team ENG --team OPS   # replace the whole team set (--label and --initiative replace likewise)
 linear project comment list <project>                         # list the project's discussion thread (UUID, slug, or name)
 linear project comment add <project> --body "Kickoff Monday"  # comment on a project
 linear project comment add <project> --body "+1" --reply-to <commentId>  # reply in a thread
diff --git a/docs/usage.md b/docs/usage.md
index 2982021b..1356845c 100644
--- a/docs/usage.md
+++ b/docs/usage.md
@@ -317,6 +317,15 @@ linear project update PROJECT-ID --content-file overview.md
 
 # Remove the lead, start date, or target date (each conflicts with its set flag)
 linear project update PROJECT-ID --clear-lead --clear-start-date --clear-target-date
+
+# Teams, labels, and initiatives are sets. --team, --label, and --initiative
+# replace the whole set; --add-*/--remove-* change it incrementally. All are
+# repeatable, and a replace flag cannot be combined with its add/remove flags.
+linear project update PROJECT-ID --add-team OPS --remove-team APP
+linear project update PROJECT-ID --add-label Launch --remove-label Beta
+linear project update PROJECT-ID --add-initiative "Q4 Bets"     # ID, slug, or name
+linear project update PROJECT-ID --initiative "Q4 Bets" --initiative "Platform"  # exactly these
+# Removing a team, label, or initiative the project does not have is an error.
 ```
 
 #### list projects
diff --git a/skills/linear-cli/references/organization-features.md b/skills/linear-cli/references/organization-features.md
index 318c6c3a..2d2328f2 100644
--- a/skills/linear-cli/references/organization-features.md
+++ b/skills/linear-cli/references/organization-features.md
@@ -56,6 +56,15 @@ linear project view <id>
 linear project create --name "New Feature" --team DEV
 linear project create --name "Q1 Work" --team DEV --initiative "Q1 Goals"
 linear project create -i  # Interactive mode
+
+# Change a project's teams, labels, or initiatives incrementally
+linear project update <id> --add-team OPS --remove-team APP
+linear project update <id> --add-label "Launch" --remove-label "Beta"
+linear project update <id> --add-initiative "Q1 Goals"   # ID, slug, or name
+
+# Replace a whole set (cannot be combined with that set's --add-*/--remove-*)
+linear project update <id> --team DEV --team OPS
+linear project update <id> --initiative "Q1 Goals" --initiative "Platform"
 ```
 
 ## Bulk Operations
diff --git a/skills/linear-cli/references/project.md b/skills/linear-cli/references/project.md
index 78715273..1ec28cfb 100644
--- a/skills/linear-cli/references/project.md
+++ b/skills/linear-cli/references/project.md
@@ -191,23 +191,37 @@ Description:
 
 Options:
 
-  -h, --help                             - Show this help.                                                             
-  --workspace             <slug>         - Target workspace (uses credentials)                                         
-  -n, --name              <name>         - Project name                                                                
-  -d, --description       <description>  - Project description (max 255 characters, enforced by Linear's API)          
-  -f, --description-file  <path>         - Read project description from file (still subject to the 255-character API  
-                                           limit)                                                                      
-  --content               <markdown>     - Project overview markdown                                                   
-  --content-file          <path>         - Read project overview markdown from a file                                  
-  -s, --status            <status>       - Status (planned, started, paused, completed, canceled, backlog)             
-  -l, --lead              <lead>         - Project lead (username, email, or @me). Use --clear-lead to remove it       
-  --clear-lead                           - Remove the project's lead (cannot be combined with --lead)                  
-  --start-date            <startDate>    - Start date (YYYY-MM-DD). Use --clear-start-date to remove it                
-  --clear-start-date                     - Remove the project's start date (cannot be combined with --start-date)      
-  --target-date           <targetDate>   - Target date (YYYY-MM-DD). Use --clear-target-date to remove it              
-  --clear-target-date                    - Remove the project's target date (cannot be combined with --target-date)    
-  -t, --team              <team>         - Team key, name, or ID (can be repeated for multiple teams)                  
-  --label                 <label>        - Replace the project's labels. May be repeated to set multiple labels.
+  -h, --help                             - Show this help.                                                                  
+  --workspace             <slug>         - Target workspace (uses credentials)                                              
+  -n, --name              <name>         - Project name                                                                     
+  -d, --description       <description>  - Project description (max 255 characters, enforced by Linear's API)               
+  -f, --description-file  <path>         - Read project description from file (still subject to the 255-character API       
+                                           limit)                                                                           
+  --content               <markdown>     - Project overview markdown                                                        
+  --content-file          <path>         - Read project overview markdown from a file                                       
+  -s, --status            <status>       - Status (planned, started, paused, completed, canceled, backlog)                  
+  -l, --lead              <lead>         - Project lead (username, email, or @me). Use --clear-lead to remove it            
+  --clear-lead                           - Remove the project's lead (cannot be combined with --lead)                       
+  --start-date            <startDate>    - Start date (YYYY-MM-DD). Use --clear-start-date to remove it                     
+  --clear-start-date                     - Remove the project's start date (cannot be combined with --start-date)           
+  --target-date           <targetDate>   - Target date (YYYY-MM-DD). Use --clear-target-date to remove it                   
+  --clear-target-date                    - Remove the project's target date (cannot be combined with --target-date)         
+  -t, --team              <team>         - Team key, name, or ID; replaces the project's entire team set. May be repeated.  
+                                           Use --add-team/--remove-team to change teams incrementally.                      
+  --add-team              <team>         - Add a team to the project, keeping its existing teams. May be repeated.          
+  --remove-team           <team>         - Remove a team from the project, keeping its other teams. May be repeated.        
+  --label                 <label>        - Project label; replaces the project's entire label set. May be repeated. Use     
+                                           --add-label/--remove-label to change labels incrementally.                       
+  --add-label             <label>        - Add a label to the project, keeping its existing labels. May be repeated.        
+  --remove-label          <label>        - Remove a label from the project, keeping its other labels (does not delete the   
+                                           label). May be repeated.                                                         
+  --initiative            <initiative>   - Initiative ID, slug, or name; replaces the project's entire initiative set. May  
+                                           be repeated. Use --add-initiative/--remove-initiative to change initiatives      
+                                           incrementally.                                                                   
+  --add-initiative        <initiative>   - Add the project to an initiative, keeping its existing initiatives. May be       
+                                           repeated.                                                                        
+  --remove-initiative     <initiative>   - Remove the project from an initiative, keeping its other initiatives (does not   
+                                           delete the initiative). May be repeated.
 ```
 
 ### view
diff --git a/src/commands/project/project-update.ts b/src/commands/project/project-update.ts
index 3cfb7f49..a1f585c1 100644
--- a/src/commands/project/project-update.ts
+++ b/src/commands/project/project-update.ts
@@ -2,9 +2,12 @@ import { Command } from "@cliffy/command"
 import { gql } from "../../__codegen__/gql.ts"
 import type { ProjectUpdateInput } from "../../__codegen__/graphql.ts"
 import { getGraphQLClient } from "../../utils/graphql.ts"
+import type { GraphQLClient } from "graphql-request"
 import {
   getProjectLabelIdByName,
+  isLinearUuid,
   lookupUserId,
+  resolveInitiativeId,
   resolveProjectId,
   resolveTeams,
 } from "../../utils/linear.ts"
@@ -50,6 +53,102 @@ const GetProjectStatuses = gql(`
   }
 `)
 
+// ProjectUpdateInput only has replace-style teamIds/labelIds, so --add-*/
+// --remove-* read the current set, compute the new one, and send the full
+// set. Each connection is paginated: a project with more than one page must
+// never have its later pages silently dropped from the replacement set.
+const GetProjectTeamsForUpdate = gql(`
+  query GetProjectTeamsForUpdate($id: String!, $after: String) {
+    project(id: $id) {
+      teams(first: 250, after: $after) {
+        nodes {
+          id
+          key
+          name
+        }
+        pageInfo {
+          hasNextPage
+          endCursor
+        }
+      }
+    }
+  }
+`)
+
+const GetProjectLabelsForUpdate = gql(`
+  query GetProjectLabelsForUpdate($id: String!, $after: String) {
+    project(id: $id) {
+      labels(first: 250, after: $after) {
+        nodes {
+          id
+          name
+        }
+        pageInfo {
+          hasNextPage
+          endCursor
+        }
+      }
+    }
+  }
+`)
+
+// Initiative membership is a join row (InitiativeToProject) with no field on
+// ProjectUpdateInput; the row id is what the delete mutation needs. name/url
+// are selected so an initiative-only update can print the success line
+// without sending an empty projectUpdate.
+const GetProjectInitiativeLinksForUpdate = gql(`
+  query GetProjectInitiativeLinksForUpdate($id: String!, $after: String) {
+    project(id: $id) {
+      id
+      name
+      url
+      initiativeToProjects(first: 250, after: $after) {
+        nodes {
+          id
+          initiative {
+            id
+            name
+          }
+        }
+        pageInfo {
+          hasNextPage
+          endCursor
+        }
+      }
+    }
+  }
+`)
+
+// resolveInitiativeId passes a UUID through unchecked. Links are deleted
+// before new ones are created, so an unknown UUID must be caught here or a
+// replace would drop the old links and then fail to add the new one.
+const GetInitiativeByIdForUpdate = gql(`
+  query GetInitiativeByIdForUpdate($id: ID!) {
+    initiatives(filter: { id: { eq: $id } }) {
+      nodes {
+        id
+        name
+      }
+    }
+  }
+`)
+
+const AddProjectToInitiativeForUpdate = gql(`
+  mutation AddProjectToInitiativeForUpdate($input: InitiativeToProjectCreateInput!) {
+    initiativeToProjectCreate(input: $input) {
+      success
+    }
+  }
+`)
+
+const RemoveProjectFromInitiativeForUpdate = gql(`
+  mutation RemoveProjectFromInitiativeForUpdate($id: String!) {
+    initiativeToProjectDelete(id: $id) {
+      success
+    }
+  }
+`)
+
 const STATUS_TYPE_MAPPING: Record<string, string> = {
   "planned": "planned",
   "in progress": "started",
@@ -60,6 +159,247 @@ const STATUS_TYPE_MAPPING: Record<string, string> = {
   "backlog": "backlog",
 }
 
+type Page<T> = {
+  nodes: T[]
+  pageInfo: { hasNextPage: boolean; endCursor?: string | null }
+}
+
+/** Follow a connection's cursor until every page has been read. */
+async function fetchAllPages<T extends { id: string }>(
+  fetchPage: (after: string | null) => Promise<Page<T>>,
+): Promise<T[]> {
+  const nodes: T[] = []
+  const seen = new Set<string>()
+  let after: string | null = null
+  while (true) {
+    const page: Page<T> = await fetchPage(after)
+    for (const node of page.nodes) {
+      if (seen.has(node.id)) continue
+      seen.add(node.id)
+      nodes.push(node)
+    }
+    if (!page.pageInfo.hasNextPage) return nodes
+    if (page.pageInfo.endCursor == null) {
+      throw new CliError(
+        "Linear reported another page of results but returned no cursor to fetch it",
+      )
+    }
+    if (page.pageInfo.endCursor === after) {
+      throw new CliError(
+        "Linear reported another page of results but returned the same cursor again",
+      )
+    }
+    after = page.pageInfo.endCursor
+  }
+}
+
+/** A user-supplied reference resolved to an id, keeping the reference for messages. */
+type ResolvedRef = { id: string; label: string }
+
+/**
+ * Apply --add/--remove to a collection: current order is kept, removed ids
+ * are dropped, added ids not already present are appended in flag order. A
+ * removal that is not in the current set throws before anything is sent.
+ */
+function applyCollectionEdit(opts: {
+  current: readonly string[]
+  add: readonly ResolvedRef[]
+  remove: readonly ResolvedRef[]
+  onMissing: (ref: ResolvedRef) => Error
+}): string[] {
+  const currentSet = new Set(opts.current)
+  for (const ref of opts.remove) {
+    if (!currentSet.has(ref.id)) throw opts.onMissing(ref)
+  }
+  const removeIds = new Set(opts.remove.map((r) => r.id))
+  const result = opts.current.filter((id) => !removeIds.has(id))
+  for (const ref of opts.add) {
+    if (!result.includes(ref.id)) result.push(ref.id)
+  }
+  return result
+}
+
+function rejectAddRemoveOverlap(
+  kind: "team" | "label" | "initiative",
+  add: readonly ResolvedRef[],
+  remove: readonly ResolvedRef[],
+): void {
+  const removeIds = new Set(remove.map((r) => r.id))
+  if (add.some((r) => removeIds.has(r.id))) {
+    throw new ValidationError(
+      `Cannot add and remove the same ${kind} in one update`,
+      {
+        suggestion:
+          `Remove the duplicate ${kind} from either --add-${kind} or --remove-${kind}.`,
+      },
+    )
+  }
+}
+
+function rejectReplaceWithIncremental(
+  kind: "team" | "label" | "initiative",
+  replace: readonly string[] | undefined,
+  add: readonly string[] | undefined,
+  remove: readonly string[] | undefined,
+): void {
+  if (replace != null && (add != null || remove != null)) {
+    throw new ValidationError(
+      `Cannot combine --${kind} with --add-${kind} or --remove-${kind}`,
+      {
+        suggestion:
+          `--${kind} replaces the project's entire ${kind} set. Use it alone to set the exact set, or use --add-${kind}/--remove-${kind} alone to change it incrementally.`,
+      },
+    )
+  }
+}
+
+/** Resolve project label names to ids, deduped by id, erroring on unknown names. */
+async function resolveProjectLabels(
+  names: readonly string[],
+): Promise<ResolvedRef[]> {
+  const resolved: ResolvedRef[] = []
+  for (const name of names) {
+    const id = await getProjectLabelIdByName(name)
+    if (!id) {
+      throw new NotFoundError("Project label", name)
+    }
+    if (!resolved.some((r) => r.id === id)) {
+      resolved.push({ id, label: name })
+    }
+  }
+  return resolved
+}
+
+async function resolveInitiatives(
+  client: GraphQLClient,
+  references: readonly string[],
+): Promise<ResolvedRef[]> {
+  const resolved: ResolvedRef[] = []
+  for (const reference of references) {
+    let ref: ResolvedRef
+    if (isLinearUuid(reference)) {
+      const data = await client.request(GetInitiativeByIdForUpdate, {
+        id: reference,
+      })
+      const initiative = data.initiatives.nodes[0]
+      if (initiative == null) {
+        throw new NotFoundError("Initiative", reference, {
+          suggestion:
+            "Pass an initiative UUID, slug ID, or exact initiative name.",
+        })
+      }
+      ref = { id: initiative.id, label: initiative.name }
+    } else {
+      ref = { id: await resolveInitiativeId(reference), label: reference }
+    }
+    if (!resolved.some((r) => r.id === ref.id)) {
+      resolved.push(ref)
+    }
+  }
+  return resolved
+}
+
+type InitiativeChange =
+  | { kind: "add"; initiativeId: string; label: string }
+  | { kind: "remove"; linkId: string; initiativeId: string; label: string }
+
+function describeInitiativeChange(change: InitiativeChange): string {
+  return change.kind === "add"
+    ? `added "${change.label}"`
+    : `removed "${change.label}"`
+}
+
+// By UUID: initiative names are not unique and the resolver rejects an
+// ambiguous name, so a name here could make the suggested command unrunnable.
+function initiativeChangeFlag(change: InitiativeChange): string {
+  return change.kind === "add"
+    ? `--add-initiative ${change.initiativeId}`
+    : `--remove-initiative ${change.initiativeId}`
+}
+
+/**
+ * Apply initiative link changes one mutation at a time. Linear has no
+ * transaction across join-row mutations, so a failure part-way leaves earlier
+ * changes applied; the error says exactly which, and which are still pending,
+ * instead of implying a rollback or that the identical command is safe to
+ * re-run (a completed --remove-initiative would fail its presence check).
+ * A request that throws may have been committed before the reply was lost,
+ * so that change is reported as unknown rather than as not applied.
+ */
+async function applyInitiativeChanges(
+  client: GraphQLClient,
+  projectId: string,
+  changes: readonly InitiativeChange[],
+  // Work already committed before these changes started (the projectUpdate
+  // for the other fields), so the failure report never reads as "no effect".
+  priorApplied: string | undefined,
+): Promise<void> {
+  const fail = (
+    applied: number,
+    outcome: "rejected" | "unknown",
+    cause: unknown,
+  ): CliError => {
+    const done = [
+      ...priorApplied != null ? [priorApplied] : [],
+      ...changes.slice(0, applied).map(describeInitiativeChange),
+    ]
+    const current = changes[applied]
+    const rest = changes.slice(applied + 1)
+    const unknownText = outcome === "unknown"
+      ? ` Unknown (the request failed before Linear answered): ${
+        describeInitiativeChange(current)
+      }.`
+      : ""
+    const notApplied = outcome === "unknown" ? rest : [current, ...rest]
+    const notAppliedText = notApplied.length > 0
+      ? ` Not applied: ${notApplied.map(describeInitiativeChange).join(", ")}.`
+      : ""
+    const remaining = [current, ...rest].map(initiativeChangeFlag).join(" ")
+    return new CliError(
+      `Failed to update project initiatives after ${applied} of ${changes.length} changes; earlier changes were not rolled back. Applied: ${
+        done.length > 0 ? done.join(", ") : "none"
+      }.${unknownText}${notAppliedText}`,
+      {
+        suggestion: outcome === "unknown"
+          ? `Check the project's initiatives, then re-run with only the remaining changes (${remaining}), or use --initiative to set the exact set.`
+          : `Re-run with only the remaining changes (${remaining}), or use --initiative to set the exact set.`,
+        cause,
+      },
+    )
+  }
+
+  let applied = 0
+  for (const change of changes) {
+    let success: boolean
+    try {
+      if (change.kind === "add") {
+        const result = await client.request(AddProjectToInitiativeForUpdate, {
+          input: { initiativeId: change.initiativeId, projectId },
+        })
+        success = result.initiativeToProjectCreate.success
+      } else {
+        const result = await client.request(
+          RemoveProjectFromInitiativeForUpdate,
+          { id: change.linkId },
+        )
+        success = result.initiativeToProjectDelete.success
+      }
+    } catch (cause) {
+      throw fail(applied, "unknown", cause)
+    }
+    if (!success) {
+      throw fail(
+        applied,
+        "rejected",
+        new CliError(
+          `Linear reported failure for initiative "${change.label}"`,
+        ),
+      )
+    }
+    applied++
+  }
+}
+
 export const updateCommand = new Command()
   .name("update")
   .description(withMarkdownHint("Update a Linear project"))
@@ -108,12 +448,47 @@ export const updateCommand = new Command()
   )
   .option(
     "-t, --team <team:string>",
-    "Team key, name, or ID (can be repeated for multiple teams)",
+    "Team key, name, or ID; replaces the project's entire team set. May be repeated. Use --add-team/--remove-team to change teams incrementally.",
+    { collect: true },
+  )
+  .option(
+    "--add-team <team:string>",
+    "Add a team to the project, keeping its existing teams. May be repeated.",
+    { collect: true },
+  )
+  .option(
+    "--remove-team <team:string>",
+    "Remove a team from the project, keeping its other teams. May be repeated.",
     { collect: true },
   )
   .option(
     "--label <label:string>",
-    "Replace the project's labels. May be repeated to set multiple labels.",
+    "Project label; replaces the project's entire label set. May be repeated. Use --add-label/--remove-label to change labels incrementally.",
+    { collect: true },
+  )
+  .option(
+    "--add-label <label:string>",
+    "Add a label to the project, keeping its existing labels. May be repeated.",
+    { collect: true },
+  )
+  .option(
+    "--remove-label <label:string>",
+    "Remove a label from the project, keeping its other labels (does not delete the label). May be repeated.",
+    { collect: true },
+  )
+  .option(
+    "--initiative <initiative:string>",
+    "Initiative ID, slug, or name; replaces the project's entire initiative set. May be repeated. Use --add-initiative/--remove-initiative to change initiatives incrementally.",
+    { collect: true },
+  )
+  .option(
+    "--add-initiative <initiative:string>",
+    "Add the project to an initiative, keeping its existing initiatives. May be repeated.",
+    { collect: true },
+  )
+  .option(
+    "--remove-initiative <initiative:string>",
+    "Remove the project from an initiative, keeping its other initiatives (does not delete the initiative). May be repeated.",
     { collect: true },
   )
   .action(
@@ -132,7 +507,14 @@ export const updateCommand = new Command()
         targetDate,
         clearTargetDate,
         team: teams,
+        addTeam,
+        removeTeam,
         label: labels,
+        addLabel,
+        removeLabel,
+        initiative: initiatives,
+        addInitiative,
+        removeInitiative,
       },
       projectId,
     ) => {
@@ -148,13 +530,16 @@ export const updateCommand = new Command()
           content == null && contentFile == null && !status &&
           !lead && !clearLead && !startDate && !clearStartDate &&
           !targetDate && !clearTargetDate &&
-          (!teams || teams.length === 0) && (!labels || labels.length === 0)
+          teams == null && addTeam == null && removeTeam == null &&
+          labels == null && addLabel == null && removeLabel == null &&
+          initiatives == null && addInitiative == null &&
+          removeInitiative == null
         ) {
           throw new ValidationError(
             "At least one update option must be provided",
             {
               suggestion:
-                "Use --name, --description, --description-file, --content, --content-file, --status, --lead, --clear-lead, --start-date, --clear-start-date, --target-date, --clear-target-date, --team, or --label",
+                "Use --name, --description, --description-file, --content, --content-file, --status, --lead, --clear-lead, --start-date, --clear-start-date, --target-date, --clear-target-date, --team, --add-team, --remove-team, --label, --add-label, --remove-label, --initiative, --add-initiative, or --remove-initiative",
             },
           )
         }
@@ -189,13 +574,26 @@ export const updateCommand = new Command()
           )
         }
 
-        if (labels) {
-          for (const label of labels) {
-            if (label.trim() === "") {
-              throw new ValidationError("Project label cannot be empty", {
-                suggestion: 'Provide a label name, e.g. --label "My Label".',
-              })
-            }
+        rejectReplaceWithIncremental("team", teams, addTeam, removeTeam)
+        rejectReplaceWithIncremental("label", labels, addLabel, removeLabel)
+        rejectReplaceWithIncremental(
+          "initiative",
+          initiatives,
+          addInitiative,
+          removeInitiative,
+        )
+
+        for (
+          const label of [
+            ...labels ?? [],
+            ...addLabel ?? [],
+            ...removeLabel ?? [],
+          ]
+        ) {
+          if (label.trim() === "") {
+            throw new ValidationError("Project label cannot be empty", {
+              suggestion: 'Provide a label name, e.g. --label "My Label".',
+            })
           }
         }
 
@@ -271,40 +669,180 @@ export const updateCommand = new Command()
           input.leadId = leadId
         }
 
-        if (teams && teams.length > 0) {
+        if (teams != null) {
           input.teamIds = (await resolveTeams(teams)).map((t) => t.id)
+        } else if (addTeam != null || removeTeam != null) {
+          const toRef = (t: { id: string; key: string }): ResolvedRef => ({
+            id: t.id,
+            label: t.key,
+          })
+          const added = (await resolveTeams(addTeam ?? [])).map(toRef)
+          const removed = (await resolveTeams(removeTeam ?? [])).map(toRef)
+          rejectAddRemoveOverlap("team", added, removed)
+          const current = await fetchAllPages(async (after) => {
+            const data = await client.request(GetProjectTeamsForUpdate, {
+              id: resolvedId,
+              after,
+            })
+            return data.project.teams
+          })
+          const teamIds = applyCollectionEdit({
+            current: current.map((t) => t.id),
+            add: added,
+            remove: removed,
+            onMissing: (ref) =>
+              new ValidationError(
+                `Cannot remove team "${ref.label}": it is not on this project`,
+                {
+                  suggestion: `Current teams: ${
+                    current.map((t) => `${t.key} (${t.name})`).join(", ")
+                  }. Use --add-team to add one.`,
+                },
+              ),
+          })
+          // Verified against the API: projectUpdate rejects teamIds: [] with
+          // "teamIds must contain at least 1 elements".
+          if (teamIds.length === 0) {
+            throw new ValidationError(
+              "Removing these teams would leave the project with no teams; Linear requires at least one",
+              {
+                suggestion:
+                  "Keep at least one team, or use --team to replace the set.",
+              },
+            )
+          }
+          input.teamIds = teamIds
         }
 
-        if (labels && labels.length > 0) {
+        if (labels != null) {
           // Replace the project's labels with exactly the resolved set,
           // matching `project update --team` and `issue update --label`.
-          const labelIds: string[] = []
-          const seen = new Set<string>()
-          for (const label of labels) {
-            const labelId = await getProjectLabelIdByName(label)
-            if (!labelId) {
-              spinner?.stop()
-              throw new NotFoundError("Project label", label)
-            }
-            if (!seen.has(labelId)) {
-              seen.add(labelId)
-              labelIds.push(labelId)
+          input.labelIds = (await resolveProjectLabels(labels)).map((l) => l.id)
+        } else if (addLabel != null || removeLabel != null) {
+          const added = await resolveProjectLabels(addLabel ?? [])
+          const removed = await resolveProjectLabels(removeLabel ?? [])
+          rejectAddRemoveOverlap("label", added, removed)
+          const current = await fetchAllPages(async (after) => {
+            const data = await client.request(GetProjectLabelsForUpdate, {
+              id: resolvedId,
+              after,
+            })
+            return data.project.labels
+          })
+          input.labelIds = applyCollectionEdit({
+            current: current.map((l) => l.id),
+            add: added,
+            remove: removed,
+            onMissing: (ref) =>
+              new ValidationError(
+                `Cannot remove label "${ref.label}": it is not on this project`,
+                {
+                  suggestion: current.length > 0
+                    ? `Current labels: ${
+                      current.map((l) => l.name).join(", ")
+                    }. Use --add-label to add one.`
+                    : "The project has no labels. Use --add-label to add one.",
+                },
+              ),
+          })
+        }
+
+        let initiativeChanges: InitiativeChange[] = []
+        let projectFromLinks: { name: string; url: string } | undefined
+        if (
+          initiatives != null || addInitiative != null ||
+          removeInitiative != null
+        ) {
+          const replacement = initiatives != null
+            ? await resolveInitiatives(client, initiatives)
+            : undefined
+          const added = await resolveInitiatives(client, addInitiative ?? [])
+          const removed = await resolveInitiatives(
+            client,
+            removeInitiative ?? [],
+          )
+          rejectAddRemoveOverlap("initiative", added, removed)
+
+          const links = await fetchAllPages(async (after) => {
+            const data = await client.request(
+              GetProjectInitiativeLinksForUpdate,
+              { id: resolvedId, after },
+            )
+            projectFromLinks = {
+              name: data.project.name,
+              url: data.project.url,
             }
+            return data.project.initiativeToProjects
+          })
+          const currentIds = links.map((l) => l.initiative.id)
+          const desiredIds = replacement != null
+            ? replacement.map((r) => r.id)
+            : applyCollectionEdit({
+              current: currentIds,
+              add: added,
+              remove: removed,
+              onMissing: (ref) =>
+                new ValidationError(
+                  `Cannot remove initiative "${ref.label}": it is not linked to this project`,
+                  {
+                    suggestion: links.length > 0
+                      ? `Current initiatives: ${
+                        links.map((l) => l.initiative.name).join(", ")
+                      }. Use --add-initiative to link one.`
+                      : "The project is not linked to any initiative. Use --add-initiative to link one.",
+                  },
+                ),
+            })
+          const desired = new Set(desiredIds)
+          const current = new Set(currentIds)
+          const labelFor = (id: string): string =>
+            [...replacement ?? [], ...added].find((r) => r.id === id)?.label ??
+              id
+          // Deletes first: a project may appear only once in an initiative
+          // hierarchy, so moving it from an initiative to that initiative's
+          // parent or child is rejected while the old link still exists.
+          initiativeChanges = [
+            ...links.filter((l) => !desired.has(l.initiative.id)).map((l) => ({
+              kind: "remove" as const,
+              linkId: l.id,
+              initiativeId: l.initiative.id,
+              label: l.initiative.name,
+            })),
+            ...desiredIds.filter((id) => !current.has(id)).map((id) => ({
+              kind: "add" as const,
+              initiativeId: id,
+              label: labelFor(id),
+            })),
+          ]
+        }
+
+        // Everything above is resolution and validation; nothing has been
+        // sent yet. An initiative-only update has nothing for projectUpdate.
+        let project: { name: string; url: string } | undefined
+        if (Object.keys(input).length > 0) {
+          const result = await client.request(UpdateProject, {
+            id: resolvedId,
+            input,
+          })
+          if (!result.projectUpdate.success) {
+            throw new CliError("Failed to update project")
           }
-          input.labelIds = labelIds
+          const updated = result.projectUpdate.project
+          if (updated) project = { name: updated.name, url: updated.url }
+        } else {
+          project = projectFromLinks
         }
 
-        const result = await client.request(UpdateProject, {
-          id: resolvedId,
-          input,
-        })
+        await applyInitiativeChanges(
+          client,
+          resolvedId,
+          initiativeChanges,
+          Object.keys(input).length > 0
+            ? "updated the project's other fields"
+            : undefined,
+        )
         spinner?.stop()
 
-        if (!result.projectUpdate.success) {
-          throw new CliError("Failed to update project")
-        }
-
-        const project = result.projectUpdate.project
         if (project) {
           console.log(`✓ Updated project: ${project.name}`)
           if (project.url) {
diff --git a/test/commands/project/__snapshots__/project-update.test.ts.snap b/test/commands/project/__snapshots__/project-update.test.ts.snap
index 7080a982..4285bc3b 100644
--- a/test/commands/project/__snapshots__/project-update.test.ts.snap
+++ b/test/commands/project/__snapshots__/project-update.test.ts.snap
@@ -16,22 +16,36 @@ Description:
 
 Options:
 
-  -h, --help                             - Show this help.                                                             
-  -n, --name              <name>         - Project name                                                                
-  -d, --description       <description>  - Project description (max 255 characters, enforced by Linear's API)          
-  -f, --description-file  <path>         - Read project description from file (still subject to the 255-character API  
-                                           limit)                                                                      
-  --content               <markdown>     - Project overview markdown                                                   
-  --content-file          <path>         - Read project overview markdown from a file                                  
-  -s, --status            <status>       - Status (planned, started, paused, completed, canceled, backlog)             
-  -l, --lead              <lead>         - Project lead (username, email, or @me). Use --clear-lead to remove it       
-  --clear-lead                           - Remove the project's lead (cannot be combined with --lead)                  
-  --start-date            <startDate>    - Start date (YYYY-MM-DD). Use --clear-start-date to remove it                
-  --clear-start-date                     - Remove the project's start date (cannot be combined with --start-date)      
-  --target-date           <targetDate>   - Target date (YYYY-MM-DD). Use --clear-target-date to remove it              
-  --clear-target-date                    - Remove the project's target date (cannot be combined with --target-date)    
-  -t, --team              <team>         - Team key, name, or ID (can be repeated for multiple teams)                  
-  --label                 <label>        - Replace the project's labels. May be repeated to set multiple labels.       
+  -h, --help                             - Show this help.                                                                  
+  -n, --name              <name>         - Project name                                                                     
+  -d, --description       <description>  - Project description (max 255 characters, enforced by Linear's API)               
+  -f, --description-file  <path>         - Read project description from file (still subject to the 255-character API       
+                                           limit)                                                                           
+  --content               <markdown>     - Project overview markdown                                                        
+  --content-file          <path>         - Read project overview markdown from a file                                       
+  -s, --status            <status>       - Status (planned, started, paused, completed, canceled, backlog)                  
+  -l, --lead              <lead>         - Project lead (username, email, or @me). Use --clear-lead to remove it            
+  --clear-lead                           - Remove the project's lead (cannot be combined with --lead)                       
+  --start-date            <startDate>    - Start date (YYYY-MM-DD). Use --clear-start-date to remove it                     
+  --clear-start-date                     - Remove the project's start date (cannot be combined with --start-date)           
+  --target-date           <targetDate>   - Target date (YYYY-MM-DD). Use --clear-target-date to remove it                   
+  --clear-target-date                    - Remove the project's target date (cannot be combined with --target-date)         
+  -t, --team              <team>         - Team key, name, or ID; replaces the project's entire team set. May be repeated.  
+                                           Use --add-team/--remove-team to change teams incrementally.                      
+  --add-team              <team>         - Add a team to the project, keeping its existing teams. May be repeated.          
+  --remove-team           <team>         - Remove a team from the project, keeping its other teams. May be repeated.        
+  --label                 <label>        - Project label; replaces the project's entire label set. May be repeated. Use     
+                                           --add-label/--remove-label to change labels incrementally.                       
+  --add-label             <label>        - Add a label to the project, keeping its existing labels. May be repeated.        
+  --remove-label          <label>        - Remove a label from the project, keeping its other labels (does not delete the   
+                                           label). May be repeated.                                                         
+  --initiative            <initiative>   - Initiative ID, slug, or name; replaces the project's entire initiative set. May  
+                                           be repeated. Use --add-initiative/--remove-initiative to change initiatives      
+                                           incrementally.                                                                   
+  --add-initiative        <initiative>   - Add the project to an initiative, keeping its existing initiatives. May be       
+                                           repeated.                                                                        
+  --remove-initiative     <initiative>   - Remove the project from an initiative, keeping its other initiatives (does not   
+                                           delete the initiative). May be repeated.                                         
 
 "
 stderr:
@@ -109,3 +123,48 @@ https://linear.app/test/project/proj-content
 stderr:
 ""
 `;
+
+snapshot[`Project Update Command - Add Team Sends Full Team Set 1`] = `
+stdout:
+"✓ Updated project: Triad Project
+https://linear.app/test/project/triad
+"
+stderr:
+""
+`;
+
+snapshot[`Project Update Command - Replace Initiatives Creates And Deletes Links 1`] = `
+stdout:
+"✓ Updated project: Triad Project
+https://linear.app/test/project/triad
+"
+stderr:
+""
+`;
+
+snapshot[`Project Update Command - Team And Add Team Conflict 1`] = `
+stdout:
+""
+stderr:
+"✗ Failed to update project: Cannot combine --team with --add-team or --remove-team
+  --team replaces the project's entire team set. Use it alone to set the exact set, or use --add-team/--remove-team alone to change it incrementally.
+"
+`;
+
+snapshot[`Project Update Command - Label And Remove Label Conflict 1`] = `
+stdout:
+""
+stderr:
+"✗ Failed to update project: Cannot combine --label with --add-label or --remove-label
+  --label replaces the project's entire label set. Use it alone to set the exact set, or use --add-label/--remove-label alone to change it incrementally.
+"
+`;
+
+snapshot[`Project Update Command - Initiative And Add Initiative Conflict 1`] = `
+stdout:
+""
+stderr:
+"✗ Failed to update project: Cannot combine --initiative with --add-initiative or --remove-initiative
+  --initiative replaces the project's entire initiative set. Use it alone to set the exact set, or use --add-initiative/--remove-initiative alone to change it incrementally.
+"
+`;
diff --git a/test/commands/project/project-update.test.ts b/test/commands/project/project-update.test.ts
index 70edd22b..78229d23 100644
--- a/test/commands/project/project-update.test.ts
+++ b/test/commands/project/project-update.test.ts
@@ -832,3 +832,552 @@ Deno.test("Project Update Command - clear flags reject their set flags", async (
     })
   }
 })
+
+// --- collection triads: --team/--label/--initiative with --add-*/--remove-* --
+
+const TRIAD_PROJECT_ID = "550e8400-e29b-41d4-a716-446655440030"
+const INITIATIVE_A = "11111111-1111-4111-8111-111111111111"
+const INITIATIVE_B = "22222222-2222-4222-8222-222222222222"
+const INITIATIVE_C = "33333333-3333-4333-8333-333333333333"
+
+const TEAM_ENG = { id: "team-eng", key: "ENG", name: "Engineering" }
+const TEAM_OPS = { id: "team-ops", key: "OPS", name: "Operations" }
+const TEAM_APP = { id: "team-app", key: "APP", name: "App" }
+
+function resolveTeamMock(reference: string, team: typeof TEAM_ENG) {
+  return {
+    queryName: "ResolveTeam",
+    variables: { reference },
+    response: { data: { teams: { nodes: [team] } } },
+  }
+}
+
+function projectLabelMock(name: string, id: string) {
+  return {
+    queryName: "GetProjectLabelIdByName",
+    variables: { name },
+    response: { data: { projectLabels: { nodes: [{ id, name }] } } },
+  }
+}
+
+function pageInfo(endCursor?: string) {
+  return { hasNextPage: endCursor != null, endCursor: endCursor ?? null }
+}
+
+// Pinning `after` proves the cursor loop forwards the previous page's cursor.
+function projectTeamsPage(
+  after: string | null,
+  nodes: typeof TEAM_ENG[],
+  endCursor?: string,
+) {
+  return {
+    queryName: "GetProjectTeamsForUpdate",
+    variables: { id: TRIAD_PROJECT_ID, after },
+    response: {
+      data: { project: { teams: { nodes, pageInfo: pageInfo(endCursor) } } },
+    },
+  }
+}
+
+function projectLabelsPage(
+  after: string | null,
+  nodes: { id: string; name: string }[],
+  endCursor?: string,
+) {
+  return {
+    queryName: "GetProjectLabelsForUpdate",
+    variables: { id: TRIAD_PROJECT_ID, after },
+    response: {
+      data: { project: { labels: { nodes, pageInfo: pageInfo(endCursor) } } },
+    },
+  }
+}
+
+function initiativeLinksPage(
+  after: string | null,
+  nodes: { id: string; initiative: { id: string; name: string } }[],
+  endCursor?: string,
+) {
+  return {
+    queryName: "GetProjectInitiativeLinksForUpdate",
+    variables: { id: TRIAD_PROJECT_ID, after },
+    response: {
+      data: {
+        project: {
+          id: TRIAD_PROJECT_ID,
+          name: "Triad Project",
+          url: "https://linear.app/test/project/triad",
+          initiativeToProjects: { nodes, pageInfo: pageInfo(endCursor) },
+        },
+      },
+    },
+  }
+}
+
+// The exact `input` is pinned: an implementation that sends the wrong set (or
+// an additive field that does not exist on ProjectUpdateInput) cannot match.
+function updateTriadProjectMock(input: Record<string, unknown>) {
+  return {
+    queryName: "UpdateProject",
+    variables: { id: TRIAD_PROJECT_ID, input },
+    response: {
+      data: {
+        projectUpdate: {
+          success: true,
+          project: {
+            id: TRIAD_PROJECT_ID,
+            slugId: "triad",
+            name: "Triad Project",
+            description: null,
+            url: "https://linear.app/test/project/triad",
+            updatedAt: "2024-01-20T15:30:00Z",
+          },
+        },
+      },
+    },
+  }
+}
+
+function addInitiativeMock(initiativeId: string, success = true) {
+  return {
+    queryName: "AddProjectToInitiativeForUpdate",
+    variables: { input: { initiativeId, projectId: TRIAD_PROJECT_ID } },
+    response: { data: { initiativeToProjectCreate: { success } } },
+  }
+}
+
+function removeInitiativeMock(linkId: string) {
+  return {
+    queryName: "RemoveProjectFromInitiativeForUpdate",
+    variables: { id: linkId },
+    response: { data: { initiativeToProjectDelete: { success: true } } },
+  }
+}
+
+// A UUID-shaped initiative is confirmed to exist before any link is touched.
+function initiativeByIdMock(id: string, name: string | undefined) {
+  return {
+    queryName: "GetInitiativeByIdForUpdate",
+    variables: { id },
+    response: {
+      data: { initiatives: { nodes: name == null ? [] : [{ id, name }] } },
+    },
+  }
+}
+
+/** Run the command against a mock server, capturing stdout, stderr, and exit. */
+async function runTriad(
+  mocks: ConstructorParameters<typeof MockLinearServer>[0],
+  args: string[],
+): Promise<{ logs: string[]; errorLogs: string[]; exited: boolean }> {
+  const server = new MockLinearServer(mocks)
+  const logs: string[] = []
+  const errorLogs: string[] = []
+  const logStub = stub(console, "log", (...a: unknown[]) => {
+    logs.push(a.map(String).join(" "))
+  })
+  const errorStub = stub(console, "error", (...a: unknown[]) => {
+    errorLogs.push(a.map(String).join(" "))
+  })
+  const exitStub = stub(Deno, "exit", (_code?: number) => {
+    throw new Error("EXIT")
+  })
+  let exited = false
+  try {
+    await server.start()
+    Deno.env.set("LINEAR_GRAPHQL_ENDPOINT", server.getEndpoint())
+    Deno.env.set("LINEAR_API_KEY", "Bearer test-token")
+    await updateCommand.parse([TRIAD_PROJECT_ID, ...args])
+  } catch (e) {
+    if (!(e instanceof Error) || e.message !== "EXIT") throw e
+    exited = true
+  } finally {
+    logStub.restore()
+    errorStub.restore()
+    exitStub.restore()
+    await server.stop()
+    Deno.env.delete("LINEAR_GRAPHQL_ENDPOINT")
+    Deno.env.delete("LINEAR_API_KEY")
+  }
+  return { logs, errorLogs, exited }
+}
+
+function assertUpdated(logs: string[]) {
+  assertEquals(logs.some((l) => l.includes("✓ Updated project")), true)
+}
+
+function assertErrored(
+  result: { logs: string[]; errorLogs: string[]; exited: boolean },
+  ...fragments: string[]
+) {
+  assertEquals(result.exited, true)
+  assertEquals(result.logs.some((l) => l.includes("✓ Updated project")), false)
+  for (const fragment of fragments) {
+    assertEquals(
+      result.errorLogs.some((l) => l.includes(fragment)),
+      true,
+      `expected stderr to include ${JSON.stringify(fragment)}, got:\n${
+        result.errorLogs.join("\n")
+      }`,
+    )
+  }
+}
+
+// --add-team reads the current teams and sends current + added as the full
+// teamIds set (ProjectUpdateInput has no addedTeamIds).
+await cliffySnapshotTest({
+  name: "Project Update Command - Add Team Sends Full Team Set",
+  meta: import.meta,
+  colors: false,
+  args: [TRIAD_PROJECT_ID, "--add-team", "OPS"],
+  denoArgs: commonDenoArgs,
+  async fn() {
+    await runUpdateWithServer(
+      new MockLinearServer([
+        resolveTeamMock("OPS", TEAM_OPS),
+        projectTeamsPage(null, [TEAM_ENG]),
+        updateTriadProjectMock({ teamIds: ["team-eng", "team-ops"] }),
+      ]),
+    )
+  },
+})
+
+Deno.test("Project Update Command - remove team keeps the other teams", async () => {
+  const result = await runTriad([
+    resolveTeamMock("OPS", TEAM_OPS),
+    projectTeamsPage(null, [TEAM_ENG, TEAM_OPS]),
+    updateTriadProjectMock({ teamIds: ["team-eng"] }),
+  ], ["--remove-team", "OPS"])
+  assertUpdated(result.logs)
+})
+
+// A second page of teams must survive into the replacement set; the pinned
+// `after` cursor proves the loop asked for it.
+Deno.test("Project Update Command - add team reads every page of current teams", async () => {
+  const result = await runTriad([
+    resolveTeamMock("OPS", TEAM_OPS),
+    projectTeamsPage(null, [TEAM_ENG], "teams-cursor"),
+    projectTeamsPage("teams-cursor", [TEAM_APP]),
+    updateTriadProjectMock({ teamIds: ["team-eng", "team-app", "team-ops"] }),
+  ], ["--add-team", "OPS"])
+  assertUpdated(result.logs)
+})
+
+// A cursor that never advances would otherwise refetch the same page forever;
+// no UpdateProject mock, so the loop must exit through the error.
+Deno.test("Project Update Command - non-advancing page cursor errors instead of looping", async () => {
+  const result = await runTriad([
+    resolveTeamMock("OPS", TEAM_OPS),
+    projectTeamsPage(null, [TEAM_ENG], "stuck-cursor"),
+    projectTeamsPage("stuck-cursor", [TEAM_APP], "stuck-cursor"),
+  ], ["--add-team", "OPS"])
+  assertErrored(result, "returned the same cursor again")
+})
+
+// No UpdateProject mock: the error must fire before the mutation.
+Deno.test("Project Update Command - remove team not on the project errors", async () => {
+  const result = await runTriad([
+    resolveTeamMock("OPS", TEAM_OPS),
+    projectTeamsPage(null, [TEAM_ENG]),
+  ], ["--remove-team", "OPS"])
+  assertErrored(
+    result,
+    'Cannot remove team "OPS": it is not on this project',
+    "Current teams: ENG (Engineering)",
+  )
+})
+
+Deno.test("Project Update Command - removing the last team errors", async () => {
+  const result = await runTriad([
+    resolveTeamMock("ENG", TEAM_ENG),
+    projectTeamsPage(null, [TEAM_ENG]),
+  ], ["--remove-team", "ENG"])
+  assertErrored(
+    result,
+    "Removing these teams would leave the project with no teams",
+  )
+})
+
+// Two references resolving to one team (key and lowercase key) collapse to a
+// single id, so the overlap is detected on ids, not spelling.
+Deno.test("Project Update Command - same team in add and remove errors", async () => {
+  const result = await runTriad([
+    {
+      queryName: "ResolveTeam",
+      response: { data: { teams: { nodes: [TEAM_OPS] } } },
+    },
+  ], ["--add-team", "OPS", "--remove-team", "ops"])
+  assertErrored(result, "Cannot add and remove the same team in one update")
+})
+
+// Adding a label already on the project is a no-op (no duplicate id), and a
+// removal in the same update is applied to the same computed set.
+Deno.test("Project Update Command - add and remove labels together", async () => {
+  const result = await runTriad([
+    projectLabelMock("Frontend", "label-frontend"),
+    projectLabelMock("Backend", "label-backend"),
+    projectLabelsPage(null, [
+      { id: "label-frontend", name: "Frontend" },
+      { id: "label-backend", name: "Backend" },
+      { id: "label-launch", name: "Launch" },
+    ]),
+    updateTriadProjectMock({ labelIds: ["label-frontend", "label-launch"] }),
+  ], ["--add-label", "Frontend", "--remove-label", "Backend"])
+  assertUpdated(result.logs)
+})
+
+Deno.test("Project Update Command - add label reads every page of current labels", async () => {
+  const result = await runTriad([
+    projectLabelMock("Launch", "label-launch"),
+    projectLabelsPage(
+      null,
+      [{ id: "label-frontend", name: "Frontend" }],
+      "labels-cursor",
+    ),
+    projectLabelsPage("labels-cursor", [{
+      id: "label-backend",
+      name: "Backend",
+    }]),
+    updateTriadProjectMock({
+      labelIds: ["label-frontend", "label-backend", "label-launch"],
+    }),
+  ], ["--add-label", "Launch"])
+  assertUpdated(result.logs)
+})
+
+Deno.test("Project Update Command - remove label not on the project errors", async () => {
+  const result = await runTriad([
+    projectLabelMock("Launch", "label-launch"),
+    projectLabelsPage(null, [{ id: "label-frontend", name: "Frontend" }]),
+  ], ["--remove-label", "Launch"])
+  assertErrored(
+    result,
+    'Cannot remove label "Launch": it is not on this project',
+    "Current labels: Frontend",
+  )
+})
+
+// --initiative replaces the set through link mutations: the missing one is
+// created and the obsolete link row is deleted by its own id. There is no
+// UpdateProject mock, proving an initiative-only update skips projectUpdate.
+await cliffySnapshotTest({
+  name:
+    "Project Update Command - Replace Initiatives Creates And Deletes Links",
+  meta: import.meta,
+  colors: false,
+  args: [TRIAD_PROJECT_ID, "--initiative", INITIATIVE_B],
+  denoArgs: commonDenoArgs,
+  async fn() {
+    await runUpdateWithServer(
+      new MockLinearServer([
+        initiativeByIdMock(INITIATIVE_B, "Beta"),
+        initiativeLinksPage(null, [
+          { id: "link-a", initiative: { id: INITIATIVE_A, name: "Alpha" } },
+        ]),
+        addInitiativeMock(INITIATIVE_B),
+        removeInitiativeMock("link-a"),
+      ]),
+    )
+  },
+})
+
+Deno.test("Project Update Command - add initiative by name", async () => {
+  const result = await runTriad([
+    {
+      queryName: "ResolveInitiativeBySlug",
+      variables: { slugId: "Beta" },
+      response: { data: { initiatives: { nodes: [] } } },
+    },
+    {
+      queryName: "ResolveInitiativeByName",
+      variables: { name: "Beta" },
+      response: {
+        data: {
+          initiatives: {
+            nodes: [{ id: INITIATIVE_B, name: "Beta", slugId: "beta" }],
+          },
+        },
+      },
+    },
+    initiativeLinksPage(null, [
+      { id: "link-a", initiative: { id: INITIATIVE_A, name: "Alpha" } },
+    ]),
+    addInitiativeMock(INITIATIVE_B),
+  ], ["--add-initiative", "Beta"])
+  assertUpdated(result.logs)
+})
+
+// No mutation mocks at all: an already-linked initiative must not be re-added.
+Deno.test("Project Update Command - add already-linked initiative is a no-op", async () => {
+  const result = await runTriad([
+    initiativeByIdMock(INITIATIVE_A, "Alpha"),
+    initiativeLinksPage(null, [
+      { id: "link-a", initiative: { id: INITIATIVE_A, name: "Alpha" } },
+    ]),
+  ], ["--add-initiative", INITIATIVE_A])
+  assertUpdated(result.logs)
+})
+
+Deno.test("Project Update Command - remove initiative not linked errors", async () => {
+  const result = await runTriad([
+    initiativeByIdMock(INITIATIVE_B, "Beta"),
+    initiativeLinksPage(null, [
+      { id: "link-a", initiative: { id: INITIATIVE_A, name: "Alpha" } },
+    ]),
+  ], ["--remove-initiative", INITIATIVE_B])
+  assertErrored(
+    result,
+    'Cannot remove initiative "Beta": it is not linked to this project',
+    "Current initiatives: Alpha",
+  )
+})
+
+// Link mutations are not transactional. When the second of two reports
+// failure, the error names what was applied and what was not, and does not
+// claim success.
+Deno.test("Project Update Command - initiative failure after partial progress is reported", async () => {
+  const result = await runTriad([
+    initiativeByIdMock(INITIATIVE_B, "Beta"),
+    initiativeByIdMock(INITIATIVE_C, "Gamma"),
+    initiativeLinksPage(null, []),
+    addInitiativeMock(INITIATIVE_B),
+    addInitiativeMock(INITIATIVE_C, false),
+  ], ["--initiative", INITIATIVE_B, "--initiative", INITIATIVE_C])
+  assertErrored(
+    result,
+    "Failed to update project initiatives after 1 of 2 changes; earlier changes were not rolled back",
+    'Applied: added "Beta"',
+    'Not applied: added "Gamma"',
+  )
+})
+
+// The thrown path: the create has no mock, so the request itself rejects
+// after the delete succeeded. A lost reply may follow a committed mutation,
+// so that change is reported as unknown, not as "not applied". "1 of 2"
+// with the removal applied also pins the ordering: deletes run before
+// creates, because a project may appear only once in an initiative
+// hierarchy and a move to a parent or child initiative is rejected while
+// the old link exists.
+Deno.test("Project Update Command - thrown initiative mutation after partial progress is reported", async () => {
+  const result = await runTriad([
+    initiativeByIdMock(INITIATIVE_B, "Beta"),
+    initiativeLinksPage(null, [
+      { id: "link-a", initiative: { id: INITIATIVE_A, name: "Alpha" } },
+    ]),
+    removeInitiativeMock("link-a"),
+  ], ["--initiative", INITIATIVE_B])
+  assertErrored(
+    result,
+    "after 1 of 2 changes",
+    'Applied: removed "Alpha"',
+    'Unknown (the request failed before Linear answered): added "Beta"',
+    "Check the project's initiatives, then re-run",
+    `--add-initiative ${INITIATIVE_B}`,
+  )
+})
+
+// projectUpdate has already committed the other fields when a link mutation
+// fails, so the report must say so rather than "Applied: none".
+Deno.test("Project Update Command - initiative failure reports the already-applied project update", async () => {
+  const result = await runTriad([
+    initiativeByIdMock(INITIATIVE_B, "Beta"),
+    initiativeLinksPage(null, []),
+    updateTriadProjectMock({ name: "Renamed" }),
+  ], ["--name", "Renamed", "--add-initiative", INITIATIVE_B])
+  assertErrored(
+    result,
+    "after 0 of 1 changes",
+    "Applied: updated the project's other fields.",
+    'Unknown (the request failed before Linear answered): added "Beta"',
+  )
+})
+
+// Retry flags name initiatives by UUID: names are not unique and the
+// resolver rejects an ambiguous one, so a name could make the suggested
+// command unrunnable.
+Deno.test("Project Update Command - suggested retry flags use initiative ids", async () => {
+  const result = await runTriad([
+    initiativeByIdMock(INITIATIVE_A, "Alpha"),
+    initiativeLinksPage(null, [
+      { id: "link-a", initiative: { id: INITIATIVE_A, name: "Alpha" } },
+    ]),
+  ], ["--remove-initiative", INITIATIVE_A])
+  assertErrored(
+    result,
+    "after 0 of 1 changes",
+    "Applied: none.",
+    'Unknown (the request failed before Linear answered): removed "Alpha"',
+    `--remove-initiative ${INITIATIVE_A}`,
+  )
+})
+
+// Links are deleted before new ones are created, so an unknown UUID must be
+// rejected up front: no delete mock, so any deletion would surface as a
+// different error, and the read-back of current links never happens.
+Deno.test("Project Update Command - replace with an unknown initiative uuid errors before deleting links", async () => {
+  const result = await runTriad([
+    initiativeByIdMock(INITIATIVE_B, undefined),
+  ], ["--initiative", INITIATIVE_B])
+  assertErrored(result, `Initiative not found: ${INITIATIVE_B}`)
+})
+
+// Scalar fields, a computed team set, and an initiative link in one call:
+// one pinned UpdateProject, then the link create, then one success line.
+Deno.test("Project Update Command - combined scalar, team, and initiative update", async () => {
+  const result = await runTriad([
+    initiativeByIdMock(INITIATIVE_B, "Beta"),
+    resolveTeamMock("OPS", TEAM_OPS),
+    projectTeamsPage(null, [TEAM_ENG]),
+    initiativeLinksPage(null, []),
+    updateTriadProjectMock({
+      name: "Renamed",
+      teamIds: ["team-eng", "team-ops"],
+    }),
+    addInitiativeMock(INITIATIVE_B),
+  ], [
+    "--name",
+    "Renamed",
+    "--add-team",
+    "OPS",
+    "--add-initiative",
+    INITIATIVE_B,
+  ])
+  assertEquals(
+    result.logs.filter((l) => l.includes("✓ Updated project")).length,
+    1,
+  )
+})
+
+// Replace cannot be combined with add/remove of the same kind. Dead endpoint:
+// the error must fire before any request.
+for (
+  const [name, args] of [
+    ["Team And Add Team Conflict", ["--team", "ENG", "--add-team", "OPS"]],
+    ["Label And Remove Label Conflict", [
+      "--label",
+      "Launch",
+      "--remove-label",
+      "Beta",
+    ]],
+    ["Initiative And Add Initiative Conflict", [
+      "--initiative",
+      INITIATIVE_A,
+      "--add-initiative",
+      INITIATIVE_B,
+    ]],
+  ] as const
+) {
+  await cliffySnapshotTest({
+    name: `Project Update Command - ${name}`,
+    meta: import.meta,
+    colors: false,
+    args: [TRIAD_PROJECT_ID, ...args],
+    denoArgs: commonDenoArgs,
+    canFail: true,
+    async fn() {
+      Deno.env.set("LINEAR_GRAPHQL_ENDPOINT", "http://127.0.0.1:1")
+      Deno.env.set("LINEAR_API_KEY", "Bearer test-token")
+      await updateCommand.parse()
+    },
+  })
+}