diff --git a/formulae/terms/terms.py b/formulae/terms/terms.py
index 0462119..510f778 100644
--- a/formulae/terms/terms.py
+++ b/formulae/terms/terms.py
@@ -17,6 +17,7 @@
 from formulae.terms.variable import Variable
 
 _log = logging.getLogger("formulae")
+_NON_INTERACTABLE_TRANSFORMS = {"hsgp", "cr", "cc", "bs", "tp"}
 
 
 # XTODO: Components have 'value' and terms have 'data'... which one should be kept?
@@ -226,6 +227,13 @@ def __init__(self, *components):
         for component in components:
             if component not in self.components:
                 self.components.append(component)
+        if len(self.components) > 1:
+            for component in self.components:
+                if (
+                    isinstance(component, Call)
+                    and component.call.callee in _NON_INTERACTABLE_TRANSFORMS
+                ):
+                    raise TypeError(f"Interaction with '{component.call.callee}' is not supported.")
         self.data = None
         self.kind = None
         self.name = ":".join([str(component.name) for component in self.components])
diff --git a/tests/test_design_matrices.py b/tests/test_design_matrices.py
index ebd5b85..c01b003 100644
--- a/tests/test_design_matrices.py
+++ b/tests/test_design_matrices.py
@@ -1179,40 +1179,6 @@ def test_categorical_ordered_series():
     assert levels == list("bcd")
 
 
-def test_bs_categorical_interaction():
-    data = pd.DataFrame(
-        {
-            "state": np.tile(
-                ["lonely", "depressed", "hopeful", "stressed", "positive", "isolated"], 10
-            ),
-            "time": np.repeat(np.arange(0, 5), 12),
-        }
-    )
-
-    formula = "0 + bs(time, degree=2, df=3) : state"
-    dm = design_matrices(formula, data)
-    assert dm.common.terms["bs(time, degree=2, df=3):state"].levels == [
-        "0, depressed",
-        "0, hopeful",
-        "0, isolated",
-        "0, lonely",
-        "0, positive",
-        "0, stressed",
-        "1, depressed",
-        "1, hopeful",
-        "1, isolated",
-        "1, lonely",
-        "1, positive",
-        "1, stressed",
-        "2, depressed",
-        "2, hopeful",
-        "2, isolated",
-        "2, lonely",
-        "2, positive",
-        "2, stressed",
-    ]
-
-
 def test_calls_with_lazy_values():
     # https://github.com/bambinos/formulae/issues/87
     value = np.arange(5)
diff --git a/tests/test_resolver.py b/tests/test_resolver.py
index 7fb7946..abd7143 100644
--- a/tests/test_resolver.py
+++ b/tests/test_resolver.py
@@ -137,6 +137,13 @@ def test_term_interaction():
     assert desc == comp
 
 
+@pytest.mark.parametrize("transform", ["hsgp", "cr", "cc", "bs", "tp"])
+@pytest.mark.parametrize("operator", [":", "*"])
+def test_spline_transforms_reject_interactions(transform, operator):
+    with pytest.raises(TypeError, match=f"Interaction with '{transform}' is not supported"):
+        model_description(f"y{operator}{transform}(x)")
+
+
 def test_term_power_interaction():
     desc = model_description("x*y")
     comp = Model(