diff --git a/cfgrib/dataset.py b/cfgrib/dataset.py
index f4054d1c..900c2840 100644
--- a/cfgrib/dataset.py
+++ b/cfgrib/dataset.py
@@ -332,9 +332,9 @@ def get_values_in_order(message, shape):
 class OnDiskArray:
     index: abc.Index[T.Any, abc.Field]
     shape: T.Tuple[int, ...]
-    field_id_index: T.Dict[
-        T.Tuple[T.Any, ...], T.List[T.Union[int, T.Tuple[int, int]]]
-    ] = attr.attrib(repr=False)
+    field_id_index: T.Dict[T.Tuple[T.Any, ...], T.List[T.Union[int, T.Tuple[int, int]]]] = (
+        attr.attrib(repr=False)
+    )
     missing_value: float
     geo_ndim: int = attr.attrib(default=1, repr=False)
     dtype = np.dtype("float32")
diff --git a/cfgrib/messages.py b/cfgrib/messages.py
index f7d725fb..d2d2000a 100644
--- a/cfgrib/messages.py
+++ b/cfgrib/messages.py
@@ -468,7 +468,10 @@ def subindex(self, filter_by_keys={}, **query):
         field_ids_index = []
         for header_values, field_ids_values in self.field_ids_index:
             for idx, val in raw_query:
-                if header_values[idx] != val:
+                # Ensure that the values to be tested is a list or tuple
+                if not isinstance(val, (list, tuple)):
+                    val = [val]
+                if header_values[idx] not in val:
                     break
             else:
                 field_ids_index.append((header_values, field_ids_values))
diff --git a/tests/sample-data/era5-levels-members.nc b/tests/sample-data/era5-levels-members.nc
new file mode 100644
index 00000000..9e52bd77
Binary files /dev/null and b/tests/sample-data/era5-levels-members.nc differ
diff --git a/tests/test_30_dataset.py b/tests/test_30_dataset.py
index a61cde53..9914e482 100644
--- a/tests/test_30_dataset.py
+++ b/tests/test_30_dataset.py
@@ -13,6 +13,7 @@
 TEST_DATA_SCALAR_TIME = os.path.join(SAMPLE_DATA_FOLDER, "era5-single-level-scalar-time.grib")
 TEST_DATA_ALTERNATE_ROWS = os.path.join(SAMPLE_DATA_FOLDER, "alternate-scanning.grib")
 TEST_DATA_MISSING_VALS = os.path.join(SAMPLE_DATA_FOLDER, "fields_with_missing_values.grib")
+TEST_DATA_MULTI_PARAMS = os.path.join(SAMPLE_DATA_FOLDER, "multi_param_on_multi_dims.grib")
 
 
 def test_enforce_unique_attributes() -> None:
@@ -340,11 +341,30 @@ def test_open_fieldset_ignore_keys() -> None:
     assert "GRIB_subCentre" not in res.attributes
 
 def test_open_file() -> None:
+    res = dataset.open_file(TEST_DATA)
+
+    assert "t" in res.variables
+    assert "z" in res.variables
+
+
+def test_open_file_filter_by_keys() -> None:
     res = dataset.open_file(TEST_DATA, filter_by_keys={"shortName": "t"})
 
     assert "t" in res.variables
     assert "z" not in res.variables
 
+    res = dataset.open_file(TEST_DATA_MULTI_PARAMS)
+
+    assert "t" in res.variables
+    assert "z" in res.variables
+    assert "u" in res.variables
+
+    res = dataset.open_file(TEST_DATA_MULTI_PARAMS, filter_by_keys={"shortName": ["t", "z"]})
+
+    assert "t" in res.variables
+    assert "z" in res.variables
+    assert "u" not in res.variables
+
 
 def test_alternating_rows() -> None:
     res = dataset.open_file(TEST_DATA_ALTERNATE_ROWS)
diff --git a/tests/test_50_xarray_plugin.py b/tests/test_50_xarray_plugin.py
index 388e68cb..16d63dd8 100644
--- a/tests/test_50_xarray_plugin.py
+++ b/tests/test_50_xarray_plugin.py
@@ -10,6 +10,7 @@
 SAMPLE_DATA_FOLDER = os.path.join(os.path.dirname(__file__), "sample-data")
 TEST_DATA = os.path.join(SAMPLE_DATA_FOLDER, "regular_ll_sfc.grib")
 TEST_DATA_MISSING_VALS = os.path.join(SAMPLE_DATA_FOLDER, "fields_with_missing_values.grib")
+TEST_DATA_MULTI_PARAMS = os.path.join(SAMPLE_DATA_FOLDER, "multi_param_on_multi_dims.grib")
 
 
 def test_plugin() -> None:
@@ -29,6 +30,30 @@ def test_xr_open_dataset_file() -> None:
     assert list(ds.data_vars) == ["skt"]
 
 
+def test_xr_open_dataset_file_filter_by_keys() -> None:
+    ds = xr.open_dataset(TEST_DATA_MULTI_PARAMS, engine="cfgrib")
+
+    assert "t" in ds.data_vars
+    assert "z" in ds.data_vars
+    assert "u" in ds.data_vars
+
+    ds = xr.open_dataset(
+        TEST_DATA_MULTI_PARAMS, engine="cfgrib", filter_by_keys={"shortName": "t"}
+    )
+
+    assert "t" in ds.data_vars
+    assert "z" not in ds.data_vars
+    assert "u" not in ds.data_vars
+
+    ds = xr.open_dataset(
+        TEST_DATA_MULTI_PARAMS, engine="cfgrib", filter_by_keys={"shortName": ["t", "z"]}
+    )
+
+    assert "t" in ds.data_vars
+    assert "z" in ds.data_vars
+    assert "u" not in ds.data_vars
+
+
 def test_xr_open_dataset_file_ignore_keys() -> None:
     ds = xr.open_dataset(TEST_DATA, engine="cfgrib")
     assert "GRIB_typeOfLevel" in ds["skt"].attrs