diff --git a/jobs/templates/includes/stage-cypress-tests.groovy.j2 b/jobs/templates/includes/stage-cypress-tests.groovy.j2
--- a/jobs/templates/includes/stage-cypress-tests.groovy.j2
+++ b/jobs/templates/includes/stage-cypress-tests.groovy.j2
@@ -74,6 +74,11 @@
                   # copy database file to the one that will be used by django for that test runner
                   cp swh-web-test.sqlite3 swh-web-test{{ n }}.sqlite3
 
+                  # prevent a race condition when multiple cypress processes load the same support file in parallel
+                  # as copy operations are performed
+                  cp cypress/support/e2e.js cypress/support/e2e{{ n }}.js
+                  sed -i "s/supportFile: 'cypress\\/support\\/e2e.js'/supportFile: 'cypress\\/support\\/e2e{{ n }}.js'/" cypress.config.js
+
                   # run django server on a dedicated port for that test runner and wait for it to be up
                   python3 swh/web/manage.py runserver --nostatic --settings=swh.web.settings.tests 0.0.0.0:500{{ n }}&
                   wait-for-it -t 90 localhost:500{{ n }}