diff --git a/.github/workflows/core.yml b/.github/workflows/core.yml
index 86515d1ac9..4a8eb4eb81 100644
--- a/.github/workflows/core.yml
+++ b/.github/workflows/core.yml
@@ -7,8 +7,8 @@ on:
         description: The input Git ref to checkout
         type: string
         required: true
-      target_branch:
-        description: The target branch (usually 'main' or 'release')
+      base_ref:
+        description: The base branch ('main' or 'release')
         type: string
         required: true
       build_docs:
@@ -34,8 +34,8 @@ on:
         description: The input Git ref to checkout
         type: string
         required: true
-      target_branch:
-        description: The target branch (usually 'main' or 'release')
+      base_ref:
+        description: The base branch ('main' or 'release')
         type: string
         required: true
       build_docs:
@@ -108,7 +108,7 @@ jobs:
         with:
           os: linux
           source_ref: ${{ inputs.source_ref }}
-          base_ref: ${{ inputs.target_branch }}
+          base_ref: ${{ inputs.base_ref }}
           scalar_type: ${{ matrix.arch }}
           deps: ci
 
@@ -200,7 +200,7 @@ jobs:
           matrix.arch == 'default'
         run: |
           . venv/bin/activate
-          if [ ${{ inputs.target_branch }} = 'release' ]; then
+          if [ ${{ inputs.base_ref }} = 'release' ]; then
             GUSTO_BRANCH='main'
           else
             GUSTO_BRANCH='future'
@@ -219,7 +219,7 @@ jobs:
           matrix.arch == 'default'
         run: |
           . venv/bin/activate
-          git clone --depth 1 https://github.com/thetisproject/thetis.git thetis-repo --branch ${{ inputs.target_branch }}
+          git clone --depth 1 https://github.com/thetisproject/thetis.git thetis-repo --branch ${{ inputs.base_ref }}
           pip install --verbose ./thetis-repo
           python -m pytest -n 8 --verbose thetis-repo/test_adjoint/test_swe_adjoint.py
         timeout-minutes: 10
@@ -241,7 +241,7 @@ jobs:
           matrix.arch == 'default'
         run: |
           . venv/bin/activate
-          git clone --depth 1 https://github.com/g-adopt/g-adopt.git g-adopt-repo --branch ${{ inputs.target_branch }}
+          git clone --depth 1 https://github.com/g-adopt/g-adopt.git g-adopt-repo --branch ${{ inputs.base_ref }}
           pip install --verbose ./g-adopt-repo
           make -C g-adopt-repo/demos/mantle_convection/base_case check
         timeout-minutes: 5
@@ -281,7 +281,7 @@ jobs:
         with:
           os: macos
           source_ref: ${{ inputs.source_ref }}
-          base_ref: ${{ inputs.target_branch }}
+          base_ref: ${{ inputs.base_ref }}
           deps: check
 
       - name: Post-run cleanup
@@ -326,7 +326,7 @@ jobs:
         with:
           os: linux
           source_ref: ${{ inputs.source_ref }}
-          base_ref: ${{ inputs.target_branch }}
+          base_ref: ${{ inputs.base_ref }}
           gpu: cuda
           deps: check
 
@@ -394,7 +394,7 @@ jobs:
     name: Build documentation
     runs-on: [self-hosted, Linux]
     container:
-      image: firedrakeproject/firedrake-vanilla-default:dev-${{ inputs.target_branch }}
+      image: firedrakeproject/firedrake-vanilla-default:dev-${{ inputs.base_ref }}
     outputs:
       conclusion: ${{ steps.report_docs.outputs.conclusion }}
     steps:
@@ -421,7 +421,7 @@ jobs:
         id: build_docs
         working-directory: firedrake-repo/docs
         run: |
-          make SPHINXOPTS="-t ${{ inputs.target_branch }}" html
+          make SPHINXOPTS="-t ${{ inputs.base_ref }}" html
           make latex
           make latexpdf
           # : Copy manual to HTML tree
@@ -476,7 +476,7 @@ jobs:
     if: |
       always() &&
       inputs.deploy_website &&
-      inputs.target_branch == 'main' &&
+      inputs.base_ref == 'main' &&
       needs.build_docs.outputs.conclusion == 'success'
     permissions:
       pages: write
diff --git a/.github/workflows/pr.yml b/.github/workflows/pr.yml
index 4ea32ccce6..e4a140dcf2 100644
--- a/.github/workflows/pr.yml
+++ b/.github/workflows/pr.yml
@@ -2,14 +2,23 @@ name: Test pull request
 
 on:
   pull_request:
-    types: [ opened, synchronize, reopened, labeled ]
+    types: [ opened, synchronize, reopened, labeled, unlabeled ]
 
 jobs:
   test:
     uses: ./.github/workflows/core.yml
     with:
       source_ref: ${{ github.ref }}
-      target_branch: ${{ github.base_ref }}
+      # If not the actual target of the PR, the target branch ('main' or 'release')
+      # can be set with an appropriate label ('base:main' or 'base:release')
+      base_ref: |-
+        ${{ case(
+          contains(github.event.pull_request.labels.*.name, 'base:main'), 'main',
+          contains(github.event.pull_request.labels.*.name, 'base:release'), 'release',
+          github.base_ref == 'main', 'main',
+          github.base_ref == 'release', 'release',
+          'INVALID_BASE_REF'
+        ) }}
       # Only run macOS tests if the PR is labelled 'macOS'
       test_macos: ${{ contains(github.event.pull_request.labels.*.name, 'macOS') }}
       # Only run GPU tests if the PR is labelled 'gpu'
diff --git a/.github/workflows/push.yml b/.github/workflows/push.yml
index 6e17222d27..0b8e13419e 100644
--- a/.github/workflows/push.yml
+++ b/.github/workflows/push.yml
@@ -11,7 +11,7 @@ jobs:
     uses: ./.github/workflows/core.yml
     with:
       source_ref: ${{ github.ref_name }}
-      target_branch: ${{ github.ref_name }}
+      base_ref: ${{ github.ref_name }}
       test_macos: true
       test_gpu: true
       deploy_website: true