What is the highest number of different mates in 1 you can have in one (legal) position? A friend and I yesterday asked ourselves what the highest number of possible mates in a (legal) position is. We were able to come up with the following position which has a total of 76 unique mates in 1, but we then failed to improve upon this one.

Q3Q3/4K2Q/6R1/3R4/QB2k3/5R1N/2R5/QQ1Q1N1B w - - 0 1


Do you know if this problem ever has been solved and what the highest possible number is? It was hard for us to come up with a reasonably low upper bound so that I have no idea whether this solution is close to the maximum.
[FEN "1B1Q1Q2/2R5/pQ4QN/RB2k3/1Q5Q/N4Q2/K2Q4/6Q1 w - - 0 1 "]


105 mates — Nenad Petrovic, Sahovski Vjesnika 1947 (Chess Problem Database)

In this position any check is mate. There are 3 knight mates (c4, g4, f7), 23 discovered mates (14 moves for the rook on c7, 9 for the bishop on b5), and 79 queen mates: 1 on a1, 2 on b2, 3 on c3, 4 on c5, 6 on d4, 3 on d5, 6 on d6, 3 on e1, 2 on e2, 4 on e3, 4 on e4, 2 on e6, 4 on e7, 3 on e8, 5 on f4, 3  on f5, 6 on f6, 4 on g3, 5 on g5, 2 on g7, 3 on h2, 3 on h5, and 1 on h8, for a total of 105 mates.