diff --git a/src/pyhf/pdf.py b/src/pyhf/pdf.py
index 20123d81bb..aaf69a5c87 100644
--- a/src/pyhf/pdf.py
+++ b/src/pyhf/pdf.py
@@ -464,11 +464,10 @@ def set_poi(self, name):
             raise exceptions.InvalidModel(
                 f"The parameter of interest '{name:s}' cannot be fit as it is not declared in the model specification."
             )
-        if dict(self.modifiers).get(name, "") == "shapefactor":
-            # in the case of custom modifiers, the desired POI is in self.parameters but
-            # not in self.modifiers
+        if self.param_set(name).n_parameters > 1:
+            # multi-parameter modifiers are not supported as POIs
             raise exceptions.InvalidModel(
-                f"The parameter '{name:s}' is of type 'shapefactor' and thus cannot be used as parameter of interest."
+                f"The parameter '{name:s}' contains multiple components and is not currently supported as parameter of interest."
             )
         s = self.par_slice(name)
         assert s.stop - s.start == 1
diff --git a/tests/test_pdf.py b/tests/test_pdf.py
index 75b7957757..d0f1ac0b81 100644
--- a/tests/test_pdf.py
+++ b/tests/test_pdf.py
@@ -1356,7 +1356,7 @@ def test_shapefactor_as_poi():
 
     with pytest.raises(
         pyhf.exceptions.InvalidModel,
-        match="The parameter 'mu' is of type 'shapefactor' and thus cannot be used as "
-        "parameter of interest.",
+        match="The parameter 'mu' contains multiple components and is not currently "
+        "supported as parameter of interest.",
     ):
         pyhf.Workspace(spec).model()