diff --git a/flox/core.py b/flox/core.py
index b4e68c23f..6de0db58f 100644
--- a/flox/core.py
+++ b/flox/core.py
@@ -1310,11 +1310,12 @@ def _lazy_factorize_wrapper(*by, **kwargs):
     return group_idx
 
 
-def _factorize_multiple(by, expected_groups, by_is_dask):
+def _factorize_multiple(by, expected_groups, by_is_dask, reindex):
     kwargs = dict(
         expected_groups=expected_groups,
         axis=None,  # always None, we offset later if necessary.
         fastpath=True,
+        reindex=reindex,
     )
     if by_is_dask:
         import dask.array
@@ -1325,7 +1326,9 @@ def _factorize_multiple(by, expected_groups, by_is_dask):
             meta=np.array((), dtype=np.int64),
             **kwargs,
         )
-        found_groups = tuple(None if is_duck_dask_array(b) else pd.unique(b) for b in by)
+        found_groups = tuple(
+            None if is_duck_dask_array(b) else pd.unique(np.array(b).reshape(-1)) for b in by
+        )
         grp_shape = tuple(len(e) for e in expected_groups)
     else:
         group_idx, found_groups, grp_shape = factorize_(by, **kwargs)
@@ -1489,7 +1492,7 @@ def groupby_reduce(
     )
     if factorize_early:
         by, final_groups, grp_shape = _factorize_multiple(
-            by, expected_groups, by_is_dask=by_is_dask
+            by, expected_groups, by_is_dask=by_is_dask, reindex=reindex
         )
         expected_groups = (pd.RangeIndex(np.prod(grp_shape)),)
 
diff --git a/tests/test_xarray.py b/tests/test_xarray.py
index 5f779d0ad..fa54e4e54 100644
--- a/tests/test_xarray.py
+++ b/tests/test_xarray.py
@@ -451,3 +451,37 @@ def test_groupby_bins_indexed_coordinate():
         method="split-reduce",
     )
     xr.testing.assert_allclose(expected, actual)
+
+
+@pytest.mark.parametrize("chunk", (True, False))
+def test_mixed_grouping(chunk):
+    if not has_dask and chunk:
+        pytest.skip()
+    # regression test for https://github.com/dcherian/flox/pull/111
+    sa = 10
+    sb = 13
+    sc = 3
+
+    x = xr.Dataset(
+        {
+            "v0": xr.DataArray(
+                ((np.arange(sa * sb * sc) / sa) % 1).reshape((sa, sb, sc)),
+                dims=("a", "b", "c"),
+            ),
+            "v1": xr.DataArray((np.arange(sa * sb) % 3).reshape(sa, sb), dims=("a", "b")),
+        }
+    )
+    if chunk:
+        x["v0"] = x["v0"].chunk({"a": 5})
+
+    r = xarray_reduce(
+        x["v0"],
+        x["v1"],
+        x["v0"],
+        expected_groups=(np.arange(6), np.linspace(0, 1, num=5)),
+        isbin=[False, True],
+        func="count",
+        dim="b",
+        fill_value=0,
+    )
+    assert (r.sel(v1=[3, 4, 5]) == 0).all().data