diff --git a/ixmp4/data/db/optimization/variable/repository.py b/ixmp4/data/db/optimization/variable/repository.py
index 76aa13f3..c8bed49e 100644
--- a/ixmp4/data/db/optimization/variable/repository.py
+++ b/ixmp4/data/db/optimization/variable/repository.py
@@ -178,11 +178,14 @@ def add_data(self, variable_id: int, data: dict[str, Any] | pd.DataFrame) -> Non
 
         index_list = [column.name for column in variable.columns]
         existing_data = pd.DataFrame(variable.data)
-        if not existing_data.empty:
-            existing_data.set_index(index_list, inplace=True)
-        variable.data = (
-            data.set_index(index_list).combine_first(existing_data).reset_index()
-        ).to_dict(orient="list")  # type: ignore[assignment]
+        if index_list:
+            data = data.set_index(index_list)
+            if not existing_data.empty:
+                existing_data.set_index(index_list, inplace=True)
+        data = data.combine_first(existing_data)
+        if index_list:
+            data = data.reset_index()
+        variable.data = data.to_dict(orient="list")  # type: ignore[assignment]
 
         self.session.commit()
 
diff --git a/tests/core/test_optimization_variable.py b/tests/core/test_optimization_variable.py
index 183e65f5..0dec1d45 100644
--- a/tests/core/test_optimization_variable.py
+++ b/tests/core/test_optimization_variable.py
@@ -273,6 +273,14 @@ def test_variable_add_data(self, platform: ixmp4.Platform) -> None:
         )
         assert_unordered_equality(expected, pd.DataFrame(variable_4.data))
 
+        # Test adding to scalar variable raises
+        with pytest.raises(
+            OptimizationDataValidationError,
+            match="Trying to add data to unknown Columns!",
+        ):
+            variable_5 = run.optimization.variables.create("Variable 5")
+            variable_5.add(data={"foo": ["bar"], "levels": [1], "marginals": [0]})
+
     def test_variable_remove_data(self, platform: ixmp4.Platform) -> None:
         run = platform.runs.create("Model", "Scenario")
         indexset = run.optimization.indexsets.create("Indexset")