That is a good question. A quick glance at the wiki answer doesn't reveal much, but if you can somehow get King Ferdinand VII to accept the proposal of a commonwealth wherein he is Emperor of Mexico and King of Spain (the original proposition by the Mexican 'government', then the empire might survive. Alternatively, the second attempt, i.e. getting any Bourbon monarch to accept the throne in lieu of Ferdinand VII refusing to even acknowledge Mexico as independent, might prove to be more successful.
From what I breifly read, I think the idea of a republic similar to the USA was the popular view in Mexico during this period, and as such it served the purpose of overthrowing the empire and replacing it with a republic. I don't know if the first can survive.
What you're thinking of was the Aztec Empire, and they didn't 'let' settlers in at all, they were conquered and decimated by European diseases. Out of curiosity, what aspects of history do you know about? Is it just American history you aren't learned on?