IDEA FOR CALIFORNIA:
1. Mexican-American War starts when American filibusters declare the Republic of California in the provinces of Alta and Baja California.
2. Northerners, refusing to fight in a war which would benefit Southern slaveholders, abstain from combat in a move which has questionable legality.
3. A more unarmed Southern force sweeps some of the northernmost parts of Mexico, ending in a stalemate by the end of a year of combat. As this is going on, Congress debates whether or not the Northern States can abstain from fighting in a war (Northern US probably argues that the AOC/Constitution's mutual defense clause refers only to defensive wars, as opposed to the offensive Mexican-American War).
4. A treaty is decided that leads to the modern borders between Mexico and the United States (Treaty of Mérida? Treaty of Havana?). During these peace talks, the southern half of the Republic of California (referred to occasionally as Monterrey-California) reject statehood proposals and are recognized by both parties as an independent state.
--OPTIONAL--
5. At some point, an empire is established in Mexico that is quickly overthrown by the Mexican people. The sovereign and his/her loyal subjects take over Monterrey and declare a government-in-exile. Eventually, a joint US-Mexico coalition help restore a republican government to California.
(I still like the idea of a Mexico and America that are on good terms -- this war would probably be seen as a major squabble that marked the worst point of their joint history. It throws a nice wrench into the USA DESTROYS MEXICO!! timelines that are common, while also not having a MEXICO UBER ALLES timeline either).