Well in strict definition of the term Mexico did balkanize. Guatemala, Belize (later colonized by Britain), Honduras, El Salvador, Nicaragua, and Costa Rica where all part of "the First Mexican Empire". I am placing this in quotations because that Empire never really existed except in the minds of a few individuals.
Furthermore you have Texas which seceded and was a country of its own for a period. And also Cuba, Puerto Rico, the Philippines, plus the Caribbean Coast of Venezuela were all part of New Spain.
When placed in perspective further balkanizing Mexico seems hard. However there where a few other attempts. But as mentioned already most didn't have much chance.
Yucatan did secede but it was Mexico who re-conquered it when the elites in Yucatan asked for help. This is the only other "republic" that actually had a chance in becoming its own state. In the case of the Rio Grande Rep. and other "secessionists" movements, as already stated, it was only a matter of sticking it up to Santa Anna or whoever was in charge. The Polkos Rebellion in Puebla for example was a similar situation against the Farias government. And the pro-American Mexican Spy Company was basically a "stick it to the man" company. They would have joined any invader against any Mexican leader just for rebellion (and money's) sake.
Mexico had it quite rough in OTL.