diff --git a/.ci/assets/ci_constraints.txt b/.ci/assets/ci_constraints.txt
index 2617a408..8f41e3f6 100644
--- a/.ci/assets/ci_constraints.txt
+++ b/.ci/assets/ci_constraints.txt
@@ -2,6 +2,9 @@
 pulpcore>=3.21.30,!=3.23.*,!=3.24.*,!=3.25.*,!=3.26.*,!=3.27.*,!=3.29.*,!=3.30.*,!=3.31.*,!=3.32.*,!=3.33.*,!=3.34.*,!=3.35.*,!=3.36.*,!=3.37.*,!=3.38.*,!=3.40.*,!=3.41.*,!=3.42.*,!=3.43.*,!=3.44.*,!=3.45.*,!=3.46.*,!=3.47.*,!=3.48.*,!=3.50.*,!=3.51.*,!=3.52.*,!=3.53.*,!=3.54.*
 
 
-
 tablib!=3.6.0
 # 3.6.0: This release introduced a regression removing the "html" optional dependency.
+
+
+multidict!=6.3.0
+# This release failed the lower bounds test for some case sensitivity in CIMultiDict.
diff --git a/.github/workflows/scripts/script.sh b/.github/workflows/scripts/script.sh
index 414d98f9..0faec043 100755
--- a/.github/workflows/scripts/script.sh
+++ b/.github/workflows/scripts/script.sh
@@ -100,8 +100,11 @@ echo "::endgroup::"
 # Install test requirements
 ###########################
 
+# Carry on previous constraints (there might be no such file).
+cat *_constraints.txt > bindings_constraints.txt || true
+cat .ci/assets/ci_constraints.txt >> bindings_constraints.txt
 # Add a safeguard to make sure the proper versions of the clients are installed.
-echo "$REPORTED_STATUS" | jq -r '.versions[]|select(.package)|(.package|sub("_"; "-")) + "-client==" + .version' > bindings_constraints.txt
+echo "$REPORTED_STATUS" | jq -r '.versions[]|select(.package)|(.package|sub("_"; "-")) + "-client==" + .version' >> bindings_constraints.txt
 cmd_stdin_prefix bash -c "cat > /tmp/unittest_requirements.txt" < unittest_requirements.txt
 cmd_stdin_prefix bash -c "cat > /tmp/functest_requirements.txt" < functest_requirements.txt
 cmd_stdin_prefix bash -c "cat > /tmp/bindings_requirements.txt" < bindings_requirements.txt