diff --git a/.github/workflows/expensive-e2e-tests.yml b/.github/workflows/expensive-e2e-tests.yml
index 16090caf91..6e8af9448e 100644
--- a/.github/workflows/expensive-e2e-tests.yml
+++ b/.github/workflows/expensive-e2e-tests.yml
@@ -30,6 +30,9 @@ jobs:
           # - 10.2.4
           # - latest
       fail-fast: false
+      # Run one version at a time to avoid the issue when SMS notification are bundled together for multiple versions
+      # running at the same time (the affected test is in grafana-plugin/e2e-tests/alerts/sms.test.ts)
+      max-parallel: 1
     uses: ./.github/workflows/e2e-tests.yml
     with:
       grafana_version: ${{ matrix.grafana_version }}