Quite honestly, I'm not sure if that is a plausible question specifically because it has to do with Monster's Inc.. We don't see too many families in Monsters Inc. (other than Mike Wazowski as you pointed out) but one of the reasons this might not make sense is simply because it's a kids movie and Pixar wanted to sell a variety of merchandise.
But because I like this question let's do some reaching.
In the world of Monsters, Inc., the titular monsters have wildly varying morphologies and abilities, but they nevertheless all seem to be members of the same species; if it was a multi-species society, you'd expect to see groups of similar-looking monsters that are obviously related--but you don't. Every one is unique in some way.
Since we don't have enough info about all the Monsters Inc. itself, we should try and relate it to the next closest mythos (if you will) of Monsters and stuff that doesn't exist. I'm going to relate it to the Covenant from the Halo Universe.
If you don't have background already, the Covenant is an alliance between a number of species that the San'shyuum and Sanghelli (sorry if I misspelled them) fought and/or incorporated into their space-faring empire. My theory is that the Monsters Inc. universe also had a Covenant-type empire. This empire was not necessarily a space-faring one, but was a multi-species empire that went a step further - to be able to breed with one another despite not looking the same (examples of this exist in real life, with Lions + Tigers birthing Ligers and Tigons, etc.). The reason there is so much variation is because their genetic-code (if they have anything that resembles genes, that is) rolls a dice on what features these creatures have, and since their ancestors were very diverse (in both species and features) they look very different as a result.
I hope this is a decent explanation!