diff --git a/tests/test_add_toml_integration.py b/tests/test_add_toml_integration.py
index a0995dd..c321ee9 100644
--- a/tests/test_add_toml_integration.py
+++ b/tests/test_add_toml_integration.py
@@ -3,6 +3,8 @@
 
 from dendropy import Tree
 
+from tact.tree_util import get_tip_labels
+
 execution_number = range(2)
 
 
@@ -52,3 +54,35 @@ def test_lone_singleton(script_runner, execution_number, tmp_path, focal_clade):
     mrca_node = res.mrca(taxon_labels=all_tips)
     mrca_tips = set([x.taxon.label for x in mrca_node.leaf_iter()])
     assert all_tips == mrca_tips
+
+
+@pytest.mark.parametrize("execution_number", execution_number)
+@pytest.mark.parametrize("clades", [["A", "B"], ["A", "C"], ["B", "C"]])
+def test_poly_singleton(script_runner, execution_number, tmp_path, clades):
+    config = f"""
+    [[tact]]
+    name = "X"
+    missing = 10
+
+    [[tact.include]]
+    stem = true
+    mrca = ["{clades[0]}"]
+
+    [[tact.include]]
+    stem = true
+    mrca = ["{clades[1]}"]
+    """
+
+    backbone = "((A:1,B:1):1,C:2);"
+    res = run_tact(script_runner, tmp_path, config, backbone)
+    new_tips = set([f"X_tact_{x}" for x in range(10)])
+
+    all_tips = set()
+    for clade in clades:
+        mrca_node = None
+        all_tips.update(clade.mrca)
+        tip_node = res.mrca(taxon_labels=all_tips)
+        for nn in tip_node.ancestor_iter():
+            all_tips.update(get_tip_labels(nn))
+            mrca_node = res.mrca(taxon_labels=all_tips)
+    raise