I've read a paper (here) about archaeological evidence of a republic in the central Mexican city state of Tlaxcala. I've also read vague references to "council rule" in some postclassic Maya states but haven't been able to track anything down about the evidence for that, or how "council rule" actually meant in practice.

What kinds of nonmonarchies existed in prehispanic Mesoamerica? Were nonmonarchical states numerous or rare? (I am assuming that even if there were many nonmonarchies in absolute terms that they still made up only a very small proportion of states; if that's a false assumption correct me) Was Spanish documentation of prehispanic states spotty enough that it's hard to say, even in broad terms, how many of them were governed?