Deseret

You have to have the Mormons move into the area pre 1848, and buy the territory from the Spanish.
Once the US bought the Territory, there is no way for the Mormons to get it away from the US.
 
You mean the US doesn't balkanise as in Deseret is the only other nation or doesn't balkanise totally and ceases to exist?
As a few areas going independant and the US continuing to exist is possible.
 
The only ways for the Mormons to had a de facto independent state of Deseret is, as mentioned:

1) Buy the land from the Spanish/Mexicans first
2) US balkanization (possibly from CSA victory in Civil War)
3) Divine Intervention

Part of me wants to say "armed rebellion," but the Nauvoo Legion counted in 1857 at roughly 5,000 men. That's nothing compared to the US armed forces which would partake in the Civil War just a few years later.
 
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