diff --git a/.github/actions/doc_preview/action.yml b/.github/actions/doc_preview/action.yml
index 0c60b899fbf..6e04abd3f1f 100644
--- a/.github/actions/doc_preview/action.yml
+++ b/.github/actions/doc_preview/action.yml
@@ -29,6 +29,11 @@ runs:
         folder: ${{ inputs.source-folder }}
         target-folder: docs/pr-preview/pr-${{ inputs.pr-number }}/
         commit-message: "Deploy doc preview for PR ${{ inputs.pr-number }} (${{ github.sha }})"
+        # Every PR preview, the main docs deploy, and the coverage deploy commit to
+        # the shared gh-pages branch. Rebase onto a deployment that landed in the
+        # meantime instead of force-pushing over it, which the branch ruleset
+        # rejects (and which used to discard the other deployment).
+        force: false
 
     - name: Leave a comment after deployment
       if: ${{ github.ref_name != 'main' && !startsWith(github.ref_name, 'release/') }}
@@ -56,6 +61,7 @@ runs:
         folder: ${{ inputs.source-folder }}
         target-folder: docs/pr-preview/pr-${{ inputs.pr-number }}/
         commit-message: "Clean up doc preview for PR ${{ inputs.pr-number }} (${{ github.sha }})"
+        force: false
 
     - name: Leave a comment after removal
       if: ${{ github.ref_name == 'main' || startsWith(github.ref_name, 'release/') }}
diff --git a/.github/workflows/build-docs.yml b/.github/workflows/build-docs.yml
index bef2a7e84c0..8dcb9608186 100644
--- a/.github/workflows/build-docs.yml
+++ b/.github/workflows/build-docs.yml
@@ -357,3 +357,6 @@ jobs:
           target-folder: docs/
           commit-message: "Deploy ${{ (inputs.is-release && 'release') || 'latest' }} docs: ${{ env.CUDA_PYTHON_DOCS_GITHUB_REF }}"
           clean: false
+          # Rebase onto concurrent PR-preview or coverage deployments instead of
+          # force-pushing, which the gh-pages ruleset rejects.
+          force: false
diff --git a/.github/workflows/coverage.yml b/.github/workflows/coverage.yml
index 6015db55c9d..b336e622940 100644
--- a/.github/workflows/coverage.yml
+++ b/.github/workflows/coverage.yml
@@ -575,3 +575,6 @@ jobs:
           target-folder: docs/
           commit-message: "Deploy combined coverage (Linux + Windows): ${{ github.sha }}"
           clean: false
+          # Rebase onto concurrent docs deployments instead of force-pushing,
+          # which the gh-pages ruleset rejects.
+          force: false