diff --git a/bigframes/session.py b/bigframes/session.py
index 4c71657798..28a38f9307 100644
--- a/bigframes/session.py
+++ b/bigframes/session.py
@@ -88,6 +88,8 @@
 _BIGQUERYCONNECTION_REGIONAL_ENDPOINT = "{location}-bigqueryconnection.googleapis.com"
 _BIGQUERYSTORAGE_REGIONAL_ENDPOINT = "{location}-bigquerystorage.googleapis.com"
 
+_MAX_CLUSTER_COLUMNS = 4
+
 # TODO(swast): Need to connect to regional endpoints when performing remote
 # functions operations (BQ Connection IAM, Cloud Run / Cloud Functions).
 
@@ -356,15 +358,10 @@ def read_gbq_query(
         else:
             index_cols = list(index_col)
 
-        # Make sure we cluster by the index column so that subsequent
-        # operations are as speedy as they can be.
-        if index_cols:
-            destination: bigquery.Table | bigquery.TableReference = (
-                self._query_to_session_table(query, index_cols)
-            )
-        else:
-            _, query_job = self._start_query(query)
-            destination = query_job.destination
+        # Can't cluster since don't know if index_cols are clusterable data types
+        # TODO(tbergeron): Maybe use dryrun to determine types of index_cols to see if can cluster
+        _, query_job = self._start_query(query)
+        destination = query_job.destination
 
         # If there was no destination table, that means the query must have
         # been DDL or DML. Return some job metadata, instead.
@@ -607,7 +604,7 @@ def _read_bigquery_load_job(
             index_cols = list(index_col)
 
         if not job_config.clustering_fields and index_cols:
-            job_config.clustering_fields = index_cols
+            job_config.clustering_fields = index_cols[:_MAX_CLUSTER_COLUMNS]
 
         if isinstance(filepath_or_buffer, str):
             if filepath_or_buffer.startswith("gs://"):
@@ -724,7 +721,9 @@ def read_pandas(self, pandas_dataframe: pandas.DataFrame) -> dataframe.DataFrame
             filter(lambda name: name is not None, pandas_dataframe_copy.index.names)
         )
         index_labels = typing.cast(List[Optional[str]], index_cols)
-        cluster_cols = index_cols + [ordering_col]
+
+        # Clustering probably not needed anyways as pandas tables are small
+        cluster_cols = [ordering_col]
 
         if len(index_cols) == 0:
             # Block constructor will implicitly build default index
@@ -937,9 +936,15 @@ def _create_sequential_ordering(
             ibis.row_number().cast(ibis_dtypes.int64).name(default_ordering_name)
         )
         table = table.mutate(**{default_ordering_name: default_ordering_col})
+        clusterable_index_cols = [
+            col for col in index_cols if _can_cluster(table[col].type())
+        ]
+        cluster_cols = (clusterable_index_cols + [default_ordering_name])[
+            :_MAX_CLUSTER_COLUMNS
+        ]
         table_ref = self._query_to_session_table(
             self.ibis_client.compile(table),
-            cluster_cols=list(index_cols) + [default_ordering_name],
+            cluster_cols=cluster_cols,
         )
         table = self.ibis_client.sql(f"SELECT * FROM `{table_ref.table_id}`")
         ordering_reference = core.OrderingColumnReference(default_ordering_name)
@@ -953,6 +958,10 @@ def _create_sequential_ordering(
     def _query_to_session_table(
         self, query_text: str, cluster_cols: Iterable[str]
     ) -> bigquery.TableReference:
+        if len(list(cluster_cols)) > _MAX_CLUSTER_COLUMNS:
+            raise ValueError(
+                f"Too many cluster columns: {list(cluster_cols)}, max {_MAX_CLUSTER_COLUMNS} allowed."
+            )
         # Can't set a table in _SESSION as destination via query job API, so we
         # run DDL, instead.
         table = self._create_session_table()
@@ -1136,3 +1145,16 @@ def _start_generic_job(self, job: formatting_helpers.GenericJob):
 
 def connect(context: Optional[bigquery_options.BigQueryOptions] = None) -> Session:
     return Session(context)
+
+
+def _can_cluster(ibis_type: ibis_dtypes.DataType):
+    # https://cloud.google.com/bigquery/docs/clustered-tables
+    # Notably, float is excluded
+    return (
+        ibis_type.is_integer()
+        or ibis_type.is_string()
+        or ibis_type.is_decimal()
+        or ibis_type.is_date()
+        or ibis_type.is_timestamp()
+        or ibis_type.is_boolean()
+    )
diff --git a/tests/system/small/test_session.py b/tests/system/small/test_session.py
index 8dfd840ede..599b8aabbc 100644
--- a/tests/system/small/test_session.py
+++ b/tests/system/small/test_session.py
@@ -113,6 +113,33 @@ def test_read_gbq_w_col_order(
             ["bool_col"],
             id="non_unique_index",
         ),
+        pytest.param(
+            "{scalars_table_id}",
+            ["float64_col"],
+            id="non_unique_float_index",
+        ),
+        pytest.param(
+            "{scalars_table_id}",
+            [
+                "timestamp_col",
+                "float64_col",
+                "datetime_col",
+                "int64_too",
+            ],
+            id="multi_part_index_direct",
+        ),
+        pytest.param(
+            "SELECT * FROM {scalars_table_id}",
+            [
+                "timestamp_col",
+                "float64_col",
+                "string_col",
+                "bool_col",
+                "int64_col",
+                "int64_too",
+            ],
+            id="multi_part_index_w_query",
+        ),
     ],
 )
 def test_read_gbq_w_index_col(