Wasn't Mexico part of some Mayaincatec Republic, on account of the whole pyramid thing? At least, Tenochtitlan should be.
In the Caribbean, every island is independent. Every single one. This arose from a particularly interesting document when the New World was first discovered. The European powers, each knowing the others would race for the resources and riches of the area, signed an agreement which allowed each nation only one island in the Caribbean. At the time, it was unknown that Cuba and Hispaniola were larger than the rest, so Portugal and France, respectively, lucked out. The fact that this agreement resulted in several islands remaining unclaimed after all the major powers divided the islands amongst themselves has resulted in some unlikely colonizers, including the Mayaincatec Republic, Sweden, the Holy Russian Empire, and a band of lost Inuit. When the islands started fighting for independence, the one-island rule was deemed to apply to the new nations as well.