PA-44 flight Instructor reported an NMAC occurred while turning downwind in the traffic pattern when another aircraft entered the pattern on downwind and descended overhead the instructor's aircraft. The Flight Instructor descended immediately and performed a go-around to a landing.

Narrative

Student and I turned left crosswind and then left downwind to Runway XX at ZZZ at pattern altitude following a go-around from Runway XX. At the same time; we observe Aircraft Y on our ADS-B about 500 ft. above pattern altitude; crossing over the airport from east to west; assuming he was planning to maneuver to enter the traffic pattern via 45 entry. Once established on downwind we saw the traffic begin to descend; so I called over the radio to alert the pilot that we were already on downwind if he was planning to turn downwind. I could not hear his response but as I lost sight of him overhead us; our ADS-B showed him beginning a turn onto downwind and continued descent. I immediately descended and turned left base as soon as possible to create additional space - I did not want to turn right as he was only 100 ft. above us and slightly to the right based on ADS-B. Once I had sufficient space; I performed a go-around and completed another traffic pattern to land. If I had realized the traffic was closing on our position earlier; I would have turned away from the airport immediately and re-entered the pattern. But from our relative positions I am not sure this was possible.