diff --git a/pyomo/core/tests/unit/test_visitor.py b/pyomo/core/tests/unit/test_visitor.py
index b70996a13dc..086c57aa560 100644
--- a/pyomo/core/tests/unit/test_visitor.py
+++ b/pyomo/core/tests/unit/test_visitor.py
@@ -1822,8 +1822,9 @@ def run_walker(self, walker):
             cases = []
         else:
             # 3 sufficed through Python 3.10, but appeared to need to be
-            # raised to 5 for recent 3.11 builds (3.11.2)
-            cases = [(0, ""), (5, warn_msg)]
+            # raised to 5 for Python 3.11 builds (3.11.2), and again to
+            # 10 for Python 3.12 builds (3.12.0)
+            cases = [(0, ""), (10, warn_msg)]
 
         head_room = sys.getrecursionlimit() - get_stack_depth()
         for n, msg in cases: