diff --git a/python/lsst/dax/obscore/obscore_exporter.py b/python/lsst/dax/obscore/obscore_exporter.py
index dceb9dc..79e8aa7 100644
--- a/python/lsst/dax/obscore/obscore_exporter.py
+++ b/python/lsst/dax/obscore/obscore_exporter.py
@@ -296,7 +296,6 @@ def __init__(self, butler: Butler, config: ExporterConfig):
         self.record_factory = RecordFactory(
             config, schema, universe, spatial_plugins, exposure_region_factory
         )
-        self.overflow = False
 
     def to_parquet(self, output: str) -> None:
         """Export Butler datasets as ObsCore Data Model in parquet format.
@@ -308,7 +307,7 @@ def to_parquet(self, output: str) -> None:
         """
         compression = self.config.parquet_compression
         with ParquetWriter(output, self.schema, compression=compression) as writer:
-            for record_batch in self._make_record_batches(self.config.batch_size):
+            for record_batch, _ in self._make_record_batches(self.config.batch_size):
                 writer.write_batch(record_batch)
 
     def to_csv(self, output: str) -> None:
@@ -325,7 +324,7 @@ def to_csv(self, output: str) -> None:
         null_string = self.config.csv_null_string.encode()
         with contextlib.closing(_CSVFile(output, null_string, sep_in=b"\x1f", sep_out=b",")) as file:
             with CSVWriter(file, self.schema, write_options=options) as writer:
-                for record_batch in self._make_record_batches(self.config.batch_size):
+                for record_batch, _ in self._make_record_batches(self.config.batch_size):
                     writer.write_batch(record_batch)
 
     def to_votable(self, limit: int | None = None) -> astropy.io.votable.tree.VOTableFile:
@@ -408,14 +407,15 @@ def to_votable(self, limit: int | None = None) -> astropy.io.votable.tree.VOTabl
 
         chunks = []
         n_rows = 0
-        for record_batch in self._make_record_batches(self.config.batch_size, limit=limit):
+        overflow = False
+        for record_batch, overflow in self._make_record_batches(self.config.batch_size, limit=limit):
             table = ArrowTable.from_batches([record_batch])
             chunk = arrow_to_numpy(table)
             n_rows += len(chunk)
             chunks.append(chunk)
 
         # Report any overflow.
-        query_status = "OVERFLOW" if self.overflow else "OK"
+        query_status = "OVERFLOW" if overflow else "OK"
         info = astropy.io.votable.tree.Info(name="QUERY_STATUS", value=query_status)
         resource.infos.append(info)
 
@@ -424,9 +424,7 @@ def to_votable(self, limit: int | None = None) -> astropy.io.votable.tree.VOTabl
             table0.array = ma.hstack(chunks)
 
         # Write the output file.
-        _LOG.info(
-            "Got %d result%s%s", n_rows, "" if n_rows == 1 else "s", " (overflow)" if self.overflow else ""
-        )
+        _LOG.info("Got %d result%s%s", n_rows, "" if n_rows == 1 else "s", " (overflow)" if overflow else "")
         return votable
 
     def to_votable_file(self, output: str, limit: int | None = None) -> None:
@@ -468,12 +466,16 @@ def _make_schema(self, table_spec: ddl.TableSpec) -> Schema:
 
     def _make_record_batches(
         self, batch_size: int = 10_000, limit: int | None = None
-    ) -> Iterator[RecordBatch]:
-        """Generate batches of records to save to a file."""
+    ) -> Iterator[tuple[RecordBatch, bool]]:
+        """Generate batches of records to save to a file.
+
+        Yields the batches and a flag indicating whether an overflow condition
+        was hit.
+        """
         batch = _BatchCollector(self.schema)
 
-        # Reset overflow flag.
-        self.overflow = False
+        # Set overflow flag.
+        overflow = False
 
         collections: Any = self.config.collections
         if not collections:
@@ -525,33 +527,33 @@ def _make_record_batches(
                         if not unlimited and count == query_limit:
                             # Hit the +1 so should not add this to the batch.
                             _LOG.debug("Got one more than requested limit so dropping final record.")
-                            self.overflow = True
+                            overflow = True
                             break
 
                         batch.add_to_batch(record)
                         if batch.size >= batch_size:
                             _LOG.debug("Saving next record batch, size=%s", batch.size)
-                            yield batch.make_record_batch()
+                            yield (batch.make_record_batch(), overflow)
 
                     if not unlimited:
                         query_limit -= count
-                    if self.overflow:
+                    if overflow:
                         # We counted one too many so adjust for the log
                         # message.
                         count -= 1
 
                     _LOG.info("Copied %d records from dataset type %s", count, dataset_type_name)
 
-                    if self.overflow:
+                    if overflow:
                         # No more queries need to run.
                         # This breaks out one level of nesting.
                         break
 
-                if self.overflow:
+                if overflow:
                     # Stop further dataset type queries.
                     break
 
         # Final batch if anything is there
         if batch.size > 0:
             _LOG.debug("Saving final record batch, size=%s", batch.size)
-            yield batch.make_record_batch()
+            yield (batch.make_record_batch(), overflow)