C172S Flight Instructor reported conflict aircraft made a non standard traffic pattern entry that resulted in a NMAC.

Narrative

I was the CFI on board with 2 CFI students in the pattern at ZZZ on runway XX with one of our company aircraft doing patterns as well. We heard another aircraft call CTAF reporting 10 miles northeast inbound. That pilot (Aircraft Y) then reported that he was going to overfly the field at 4;000' to enter a left downwind runway XX. I saw the aircraft on our ADSB and that he was descending just north of the airport while we were taking off after a touch and go. I attempted to visually locate the aircraft while we were on the crosswind leg and turning downwind; but we were in a high-wing aircraft in a left turn so we could not see in the direction he was coming from.Shortly after entering the downwind leg I noticed on ADSB an aircraft at our altitude at our exact location. None of us (myself or 2 students) could see the aircraft visually and I then zoomed in on the MFD (Multi-function Flight Display) to see exactly where the other aircraft was. It was immediately behind us at the same altitude. The student flying continued to fly with myself and the student in the back seat looked back to try to find the other aircraft. We spotted it exactly at our altitude approx. 200-300' behind us.We accelerated (it was a similar type of aircraft that we were in) and I then got on the radio and asked that pilot if he had us in sight. He replied that he did. Despite the very close separation; I did not feel that evasive action was necessary due to all the factors involved.He made a full stop; after which I professionally advised him that in the future he should not descend to pattern altitude while overflying the airport and then make a left turn into the pattern; but instead should overfly above pattern altitude past the pattern and make a teardrop entry on the 45 to a downwind/