Flight Instructor reported an NMAC event during landing pattern training. The Instructor took evasive action to avoid a none reporting aircraft.

Narrative

There were three potential mid-air collisions averted today if it weren't for the actions of three separate pilots; two being Instructors and one unknown. I am an Instructor who was flying with my student for training purposes in light-moderate gusting conditions (11G17KTS) at ZZZ. Other airport conditions included VMC and 5 aircraft in the pattern. I was PNF (Pilot not Flying) as my student was (initially) at the controls.My student and I were on an extended left downwind for Runway XX at ZZZ for other traffic; which included two aircraft on final. At approximately the 1.5-mile mark from the threshold while on the downwind; I hear a traffic alert in my headset via Bluetooth from my iPad (connected to a Garmin GDL 50 for ads-b in and traffic alerting capabilities; amongst other things). I was on another screen and took a few seconds to switch to the airport map to identify where this traffic was coming from because I had accidentally inhibited the traffic alert popup; which brings attention to the traffic conflict. By the time I got to the map screen; I see a Bonanza on the display with tail number Aircraft Y coming from my right; approximately 750 ft. horizontally and 150 ft. below my aircraft (my iPad stated 200 ft.; which indicates an ads-b calculated range of 151 ft. to 250 ft.). At this moment; I take controls from the student and start a steep turn to the right. By the time this aircraft passed us; it was within 75 ft. horizontally and still 150 ft. below. After this incident; the pilot of the Bonanza had cut off a Diamond DA-20 aircraft on final; with an even closer; near miss of what was definitely less than 1;000 ft. (this Instructor later contacted me; and I found out the Bonanza was an estimated 300-500 ft. horizontally and 0 ft. vertically from his aircraft). I was watching this Bonanza pilot on my iPad during this second incident; and I can confirm that the Instructor in the Diamond aircraft swiftly veered the aircraft to the right; narrowly avoiding a second collision with this Bonanza. Instructor had advised me that he had also taken controls from his student.The third incident I did not witness; but this Instructor later told me that the Bonanza had a third incident with a Cessna in the pattern; which was also a near miss.