Yeah, like Argentina where if I recall the state governors would sometimes form alliances and conduct actions on their own. The Argentine part of the War of the Confederation against Peru-Bolivia seems like a good example. Its probably how actions against French Louisiana, British North America, and Mexico would take place, probably mixed with or part of individual filibuster attempts would take place.
Permanent fracture? There was always the slavery issue. Slavery could drive a wedge between South and North. Since slavery wasn't profitable in the North compared to the South, and the South's economy was more linked to Europe than the North, this could split the United States decisively, and only add another chapter to the American Civil Wars.
Which speaking of Argentina and Latin America, I wonder what the overall effect might be on that part of the world considering how much so many of them idolised the US.