In the UI it would be nice to duplicate the selected connection, in the menu "With Selected". 

The copy would be set with the same name plus some suffix (_copy, _1, whatever) and it is useful for when you have a connection with all equal fields except something in a particular one. 
airflow/www/views.py
"""Returns formatted dag_runs for Tree view"""
        dates = sorted(dag_runs.keys())
        min_date = min(dag_runs, default=None)
        task_instances = {
            (ti.task_id, ti.execution_date): ti
            for ti in dag.get_task_instances(start_date=min_date, end_date=base_date)
        }
        expanded = set()
        
        
        
        node_count = 0
        node_limit = 5000 / max(1, len(dag.leaves))
        def encode_ti(task_instance: Optional[models.TaskInstance]) -> Optional[List]: