I just got my first-ever 11th non-con game, with Colorado (DIII Rupp). And so I'm thinking...
Everyone gets 27 games: the 10 non-cons, the 16 conference games, and the CT first (or second) round. So we're all used to 0-27 and 35-0 as the extremes. But every year or so, a couple of teams get an 11th non-con game (it's randomly assigned and makes the scheduling robot's job easier.)
So in order to play 37, you'd need:
*An extra non-con game (10+1)
*Conference play (16)
*No bye in the first round of the CT, but make the CT final (4)
*Make the NT final (6)
...for 37 total.
Obviously 37-0 is impossible - you'd get a bye in the CT, so 36-0 would be the record. 36-1 is the same way - if you're 15-1 in conference play, you can't be on the low end of a three-way tie in your division. 35-2 (14-2), though, is possible - three teams sweeping conference play but winning at home against each other.
So 35-2 (11-0, 14-2 and a 3-seed, win the CT, win the NT) is possible, as is anything below that as far as, uh, 9-28 (0-11, 0-16 and a 6-seed, win the CT, lose the NT final).
Anyone have an example of a team that's done this?