Though I don't know if I'll ever get to a good enough state of polish to publish it here on AH.com, I've been working on a TL for quite a while which would create a North America with four Great Powers and no superpowers. My PoD is that Napoleon never reimposes slavery in St-Domingue, thus no Haitain war of independence. The 50,000 troops Napoleon has slated for stationing there and in the newly reacquired Louisana thus don't end up dying in the jungles of Hispaniola. The 35,000 of those that end up in Louisiana have to spread out and become soldier-farmers in dispersed garrisons since the colonial infrastucture isn't suited for supporting such a large standing force. This helps to increase the French colonial presence outside the nuclei of OTL southern LA and the small French settlements in OTL Missouri. Intermarriage with native women creates a large Métis class, augmented by the eventual immigration of almost 1 million Irish in the 1840s and 50s (New Orleans, not New York, was the main entrance point for Irish OTL during the Famine, due to the importance of the Liverpool-New Orleans cotton trade). Louisiana declares independence from France after the defeat of Napoleon and the Restoration of the Bourbons and become a republic.
Anyway, my TL creates a NA where the US keeps to its 1783 borders with the exception of adding East Florida (Louisiana gets West Florida to the Escambia). Louisiana, after a series of conflicts with Mexico (which it won) and Britian (which it lost) now has these borders (I don't know how to make maps, sorry):
Starting in the East and going anti-clockwise:
- the Escambia river to the 31st parallel
- the 31st parallel to the Mississippi
- the Mississippi to the Missouri
- the Missouri to the Platte
- the Platte to the 101st longitude
- the 101st longitude south to the Colorado River (the Colorado that goes through Austin, TX, not the one that carved the Grand Canyon)
- the Colorado to the Gulf
Also included in Louisiana is all of St-Domingue (Hispaniola), though the other French possessions in the Caribbean remain in French hands.
The other two powers are of course Canada (BNA), which now includes the northern part of OTL's Louisiana Purchase territory and the Oregon Country, and Mexico, which has retained most of its northern territories as well. I've only written out the TL to about 1865 (but with many holes), but each of these four countries is large enough, have large enough populations and enough resources to come into their own and eventually make their mark on the international stage. Each, though, has its own unique and varied internal problems which will hinder their development at certain stages, and that's the main reason for the blockage in my TL writing. I've got four basket-cases on my hands!
Canada is larger but and has a somewhat increased population, but a lot of that comes from Francophone Louisiana, adding to the Anglo-Franco problem (Canada will end up with a lot more Franco-majority provinces than OTL, perhaps three or four). Mexico's still got its revolving governments and the tensions between the hacendados and the peasants. Louisiana's got, in New Orleans at least, the old four-way fight between legitimists-orleanists-bonapartists-republicans (the Republic was declared in 1817 as a compromise and has never been fully excepted), and also has to deal with a society made up of Whites (French and Irish, mostly, though for the Irish the language issue never becomes a problem, since most spoke Gaelic at home and saw English as the language of the oppresors at the time]), Métis, Natives (including most of the "civilized tribes" of the US Southeast who were given sanctuary in Louisiana and granted lands in the Ozark region and have since melded very successfully into LA society), Africans and Creole Africans (the OTL
gens de couleur libres). The US, of course, is split on sectional lines as well as the growing debate on slave versus free states. When Britain, Mexico, and Louisiana all abolish slavery in the 1830s (Louisiana was also part-slave, part-free beforehand), the southern slave states become increasingly recalcitrant on the issue. Though Louisiana might now be a free country, it hadn't closed its doors to American trade, so slave-produced cotton flowed freely through the Louisiana ports of New Orleans, Mobile, and Pensacola. As long as the money's there, why rock the boat?
As you can see, I've put a lot of thought into this, so I tend to ramble. One day I'll post my TL and let everyone praise and pick it apart. The point is, though, that it'd be rather easy to create a North America where no one single nation dominates without having to resort to balkanization.