During the lengthy, somewhat acrimonious discussion about the U.S. Civil War turning into a world war and who would line up on whose side, Grimm_Reaper suggested a possible future war in which France-backed Mexican emperor Maximillian, seeking to bolster his domestic Mexican support, fought the Confederacy in order to reclaim whatever Mexican Cession territories the Confederacy inherited.
(I don't think Max "starting it" is absolutely essential. Perhaps the Confederates start it, in support of northern Mexican strongmen who want to join the Confederacy or in an attempt to get a Pacific port.)
The Confederates find the Mexicans to be a tough opponent, especially if the Mexicans start stirring up trouble with the slave population on the Gulf Coast and (this is pushing it) assisting diehard Unionists in places like East Tennessee.
The Mexicans end up advancing into the Confederacy itself. This is where the Union intervenes, seeking to reverse the results of OTL's Civil War and prevent the Mexicans from making off with more than a few scraps of "rightful" U.S. territory.
With much of the Confederacy's armed might in Texas, whatever western territories the Confederacy got from its victory, and in the Gulf region, the Union army wins a series of victories, plowing through the countryside liberating slaves and generally whipping the Confederates.
What happens when U.S. and Mexican armies meet could be interesting. I doubt the U.S. is going to want the Mexicans to get any significant amounts of territory, but Max's throne rests on his ability to avenge 1848, at least to some degree.
What do you all think of this scenario?