Spain keeps Mexico. How do the USA expand?

In our timeline, New Mexico had a larger Spanish settlement than the rest of the Mexican Cession. The Rio Grande provided a good transport there. In addition, unlike in the rest of the cession, there were the sedentary Pueblo, who could serve as labor. There was also a Spanish governor of New Mexico in the late 18th century who was able to militarily force a treaty on the Comanche that lasted for a couple of generations and made the Spanish population there grow and outnumber the Pueblo.

In addition, the Rio Grande also served as a good water source, very differently from Arizona, which was pretty much uninhabitable, at the time.
 
Mexico revolts again during an Carlist War/some other screw up back home in Spain, waves of American setters, and the USA coming to town hard on the Spanish.

There will be no Carlist war because the Liberals were crushed by design by the OP. That will erode the powerbase of Isabella II and her mother and opening the way to make Carlos the king after the death of Fernando VII unless Maria Christina gives birth to a boy, and that will probably butterfly the Carlist Wars too.
 
There will be no Carlist war because the Liberals were crushed by design by the OP. That will erode the powerbase of Isabella II and her mother and opening the way to make Carlos the king after the death of Fernando VII unless Maria Christina gives birth to a boy, and that will probably butterfly the Carlist Wars too.
Well Maria Christina having a boy will surely butterfly the Carlist Wars as Carlos has zero standing for declaring himself the rightful heir over the son of his late elder brother (as the boy will be before him in both the Salic and the male preference line of succession)
 
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