Many of them do. Sometimes you can select from a menu of pre-defined temperaments, sometimes you can individually tune each pitch class (e.g. you can tune all the G's 4 cents sharp if you want), and sometimes you can tune all 88 (or so) notes individually.

In general, you run into problems if you want more than 12 notes per octave because a) standard keyboards are really inconvenient for that and b) midi wasn't designed to support microtonal music in any consistent way, so you have to employ strange kludges, like use a separate channel for every pitch class and use pitch bend for tuning.