UPDATE #4: After some asking on Matplus a few weeks ago, I found that my 42 was already beaten. But I have an ego. It feels so good to have come so close! Anyhow, here’s the “new” records.
The 43 Mates:
Pd2-1, Pf2-2, Ph2,1, Nc3-2, Nh4-2, Qd4-4, Kf7-6, Rg5-12, Be4-13
The 44 Mates:
Pa7-1, Pd7-1, Ph7-1, Ne8-2, Qf5-4, Nd8-8, Be5-13, Rc4-14
I always knew that three pawn promotions. I just couldn’t figure it out myself. The same goes for giving the queen more moves. Another thing, quite amusing to me at the least, is that you can just add in a pawn to the 43 one to equal the record of 44 with promotions
UPDATE #3: I found 42 without extra promotions. I made that useless knight useful with 2 mates and I tacked on an extra discovered checkmate by giving the queen’s knight more freedom.
Slight Update: I found a way to keep the same result with one less pawn. I also moved the king to give the queen’s horse more room, even though it changes nothing. It’s just more elegant
The 42 Mates:
Rg2-14, Be5-13, Nc5-7 Ne8-2, Qb5-2, Ph7-1, Pa7-1, Pd3-1. Pe3-1
UPDATE #2-I’ve totally beaten that 36 with an astonishing 39! So darn close
to 40! Take a look! I shall heartily accept any flaws that you find!
If you could get 3 pawn promotion checkmates in a position that is similar to this, you could get 40, but due to the fragility of the set up, I severely doubt this. I was unable to do it myself.
The 39 Mates:
Pb7-1, Pd7-1, Pc2-1, Pe2-1, Bd4-13, Rf5-14, Ng4-6, Qh4-2
UPDATE: I have recently found a flaw Araud Mortier’s position. If the d4 bishop moves, then the black pawn can block the rook check. This also invalidated my answer as well. So I flipped the position for a new record of 36. This will no doubt be broken soon. This position is made for him.