for tii in external_tis:
                    if not dag_bag:
                        from airflow.models.dagbag import DagBag
                        dag_bag = DagBag(read_dags_from_db=True)
                    external_dag = dag_bag.get_dag(tii.dag_id, session=session)
                    if not external_dag:
                        raise AirflowException(f"Could not find dag {tii.dag_id}")
                    downstream = external_dag.partial_subset(
                        task_ids_or_regex=[tii.task_id],
                        include_upstream=False,
                        include_downstream=True,
                    )
                    result.update(
                        downstream._get_task_instances(
                            task_ids=None,
                            run_id=tii.run_id,
                            start_date=None,
                            end_date=None,
                            state=state,
                            include_subdags=include_subdags,
                            include_dependent_dags=include_dependent_dags,
                            include_parentdag=False,
                            as_pk_tuple=True,
                            exclude_task_ids=exclude_task_ids,
                            dag_bag=dag_bag,
                            session=session,
                            recursion_depth=recursion_depth + 1,
                            max_recursion_depth=max_recursion_depth,
                            visited_external_tis=visited_external_tis,
                        )