If there are a very large number of fundamental particles, it is likely that there is some reason for the number,

Could you expand on this?

The only reason I can think of is that the particles have various qualities, and we've got all the possible combinations.

I assume that there some range of numbers which suggest an underlying pattern-- it's vanishingly unlikely that there's a significance to the number of stars in the galaxy.

I think there was something in Gregory Bateson about this-- that there's a difference between a number that's part of a system (he was talking about biology, not physics) as distinct from "many".