diff --git a/aligned/data_source/batch_data_source.py b/aligned/data_source/batch_data_source.py
index dc71ddc..634609c 100644
--- a/aligned/data_source/batch_data_source.py
+++ b/aligned/data_source/batch_data_source.py
@@ -1,4 +1,5 @@
 from __future__ import annotations
+from copy import copy
 
 from typing import TYPE_CHECKING, TypeVar, Any, Callable, Coroutine
 from dataclasses import dataclass
@@ -801,8 +802,9 @@ class ColumnFeatureMappable:
     mapping_keys: dict[str, str]
 
     def with_renames(self: T, mapping_keys: dict[str, str]) -> T:
-        self.mapping_keys = mapping_keys  # type: ignore
-        return self
+        new = copy(self)
+        new.mapping_keys = mapping_keys  # type: ignore
+        return new
 
     def columns_for(self, features: list[Feature]) -> list[str]:
         return [self.mapping_keys.get(feature.name, feature.name) for feature in features]
diff --git a/aligned/tests/test_model_target.py b/aligned/tests/test_model_target.py
index 05a1c3e..a08c5be 100644
--- a/aligned/tests/test_model_target.py
+++ b/aligned/tests/test_model_target.py
@@ -99,6 +99,16 @@ class NewModel:
     assert feature.name == 'a'
 
 
+def test_with_renames() -> None:
+    from aligned import FileSource
+
+    source = FileSource.parquet_at('test_data/test_model.parquet').with_renames({'some_id': 'id'})
+    other = source.with_renames({'other_id': 'id'})
+
+    assert source.mapping_keys == {'some_id': 'id'}
+    assert other.mapping_keys == {'other_id': 'id'}
+
+
 @pytest.mark.asyncio
 async def test_model_insert_predictions() -> None:
     """
@@ -136,6 +146,43 @@ class TestModel:
     assert preds.select(expected_frame.columns).equals(expected_frame)
 
 
+@pytest.mark.asyncio
+async def test_model_insert_predictions_csv() -> None:
+    """
+    Test the insert (aka. ish append) method on the feature store.
+    """
+    from aligned import FileSource, FeatureStore
+
+    path = 'test_data/test_model.csv'
+
+    @model_contract(
+        name='test_model',
+        features=[],
+        prediction_source=FileSource.csv_at(path).with_renames({'some_id': 'id'}),
+    )
+    class TestModel:
+        id = Int32().as_entity()
+
+        a = Int32()
+
+    store = FeatureStore.experimental()
+    initial_frame = pl.DataFrame({'id': [1, 2, 3], 'a': [1, 2, 3]})
+    initial_frame.write_csv(path)
+
+    expected_frame = pl.DataFrame({'id': [1, 2, 3, 1, 2, 3], 'a': [10, 14, 20, 1, 2, 3]})
+
+    store.add_compiled_model(TestModel.compile())  # type: ignore
+
+    await store.insert_into(FeatureLocation.model('test_model'), {'id': [1, 2, 3], 'a': [10, 14, 20]})
+
+    preds = await store.model('test_model').all_predictions().to_polars()
+
+    stored_data = pl.read_csv(path).select(id=pl.col('some_id'), a=pl.col('a'))
+    assert stored_data.equals(expected_frame)
+
+    assert preds.select(expected_frame.columns).equals(expected_frame)
+
+
 @pytest.mark.asyncio
 async def test_model_upsert_predictions() -> None:
     """
diff --git a/pyproject.toml b/pyproject.toml
index e18fb32..27f723b 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -1,6 +1,6 @@
 [tool.poetry]
 name = "aligned"
-version = "0.0.75"
+version = "0.0.76"
 description = "A data managment and lineage tool for ML applications."
 authors = ["Mats E. Mollestad <mats@mollestad.no>"]
 license = "Apache-2.0"
diff --git a/test_data/test_model.csv b/test_data/test_model.csv
new file mode 100644
index 0000000..9bfa2bd
--- /dev/null
+++ b/test_data/test_model.csv
@@ -0,0 +1,7 @@
+some_id,a
+1,10
+2,14
+3,20
+1,1
+2,2
+3,3
diff --git a/test_data/test_model.parquet b/test_data/test_model.parquet
index 5bab2d3..4db5d82 100644
Binary files a/test_data/test_model.parquet and b/test_data/test_model.parquet differ