With Wilcox' permission I am posting some speculation on how South America has evolved so far, and how it can be dragged into the Great War. Hopefully this gets some discussion going:
"I am Parting from the notion that butterflies reached South America as a result of President Calhoun’s support of republican movements in the region. Two main initial changes can be observed: one, Rio Grandese gained independence from Brazil, and two - which was never mention but only seems logical - the Peru-Bolivia Confederation also received some American aid during the War of Confederation, however minimal.
Unlike The Rio Grandese Republic, the Peru-Bolivian Confederation did not survive. However upon its breakup South Peru decided to stay in federation with Bolivia. It was only the elites in Lima and North Peru - who had more to gain from trade with Chile and Colombia that opted to break away. Chile wasn’t fully defeated during the war but it didn’t come out victor as in OTL, thus it opted to shift its focus south - gain control of the straights - and west into the Pacific. This further complicates Pacific politics as we are adding Chile to the number of powers in the region California, Britain, Japan, Corea, and the US.
North Peru, simply referred to as Peru - the Confederation is commonly known Bolivia though it likely has a very long and lofty constitutional name - began focussing on maritime trade, as it was now too small for any other course. It also struck an alliance with Chile to contain Bolivia, in case some dictator ever tried to restore the Inca Empire. However, Bolivia - outmatched at sea - placed its focus inland, and expanded into the Chaco and Amazon with success. Thus explaining the huge-ass Bolivia of TTL. I am also guessing that the capital is neither Sucre, La Paz, or Cusco, but Tacna the capital of the Confederation in OTL, which lies practically on the Peru, Bolivia border and has likely grown, not just as the political capital but as an economic one since it would be Bolivia's main port as well.
On the other side of the Andes, the river Republics - Uruguay, Paraguay, and Rio-Grandese - evolved more-or-less together. Early on an alliance was likey formed to facilitate trade, and to avoid being swallowed by the larger powers - Brazil, Argentina, Bolivia - that surrounded them. An economic and military alliance soon evolved into a customs union, a trade union, and ultimately the political federation known as Mokuguay - like Bolivia I am guessing it has a loftier constitutional name - the Mesopotamia of the West. Their federation provoked the Platinean War, as the Argentinean administration feared a new power gaining control of the river trade. The Platinean war did not end up well for Argentina, resulting in the independence of Tucuman, which was rapidly brought into Bolivia’s economic influence.
In the last decades of the 19th Bolivia and Mokuguay both became formidable regional powers. With good political relations, both federations facilitated trade - liking their roads and tracks from the Rivers to the Andes to the Pacific - and secured a military alliance dragging Tucuman along. Argentina on the other hand had been humiliated, and weakened beyond near repair. In the aftermath, it signed a treaty with Chile establishing the border on the Andes’ drainage basins - but unlike OTL were the southern border was evenly split, Chile took the winning bite thus gaining full control of the Straights and access to its claims of the Falkland Islands.
Colombia and Venezuela probably re-united after the successful example of Mokuguay and Bolivia. It was also likely a result of British incursions into Venezuela. Similarly the Mesoamerican Federation was formed after the US dealings in Costa Rica. Meanwhile Brazil remains in isolation, as the only power with legal slavery. By now the aging (60+) Emperor Alfonso - I am guessing Pedro II died already since he’d be 80+ by now - is trying to figure out a way to end slavery without rocking the boat. Unfortunately, for Brazil, the boat was rocked at the outbreak of the Great War.
If the war reaches South America, you have two systems of alliances already in place: one centered in Chile with Peru, Argentina (and likely Ecuador) as its allies, and one forged between Bolivia, Mokuguay and Tucuman. CP&A have the advantage at sea, and likely have better trained officers, and perhaps better tech while BM&T have the advantage on land, as well as greater resources and manpower.
Colombia and Brazil are wild cards, but I reckon Colombia will throw its weight with Bolivia and Mokuguay, while Brazil will do its best to remain neutral.
These are only the major conflicts and movements. Smaller conflicts, crisis, border adjustments, etc. likely happened. I’m only suggesting what were likely the major divergences from OTL: a different outcome to the Confederation War, the events that led to and the result of the Platinean War, and the lack of a Pacific War until now, with the likelihood the Brazil has stayed out of the arms race. Furthermore it is simply speculation Wilcox can take his TL in any direction he please, but this makes sense to me.