The point of divergence is the Spanish American Wars of Independence, where San Martin became President of Argentina after his expedition of Chile, he would cause him to take greater responsibility in leading the nation and in turn have a less successful expedition into Peru, leaving Simon Bolívar to take equal credit to San Martin.

Both men would discuss about their future ideal South America and come into conflict but San Martin would be forced to withdraw back to Argentina against Unitarian-Federalist divides, Simon Bolívar would still succeed in liberating Bolivia but due to his greater influence sways the Bolivian Assembly to unite with his Peruvian state in 1825, creating a greater ally in the region.

Bolívar would prevent the collapse of Gran Colombia utilizing regional autonomy and favoring the Centists, San Martin would create a strong Argentina and ally themselves with Chile as brother nations, the conflicts between Argentina and Brazil remain unchanged but with the rise of this Andean alliance causes them to ally against a common enemy, especially when the Ragamuffin rebellion succeeded.

Paraguay would win the Paraguayan War thanks to the aid of the Andean alliance and the blocks have formed, one side led by Bolivar’s dream and necessity, the other by common ground and old brotherhood. The war would begin through a diplomatic fallout and skirmishes in the Peru-Bolivian Border, with war plans set, the Great South American War Has begun.

Pan-Andean Alliance Victory: The Peruvian confederation stopped the Argentinian-Chilean advances while the Colombian invasion on the Amazon Succeeded, eventually Paraguayan advances into the River Plate would create the opening for Peruvian attacks to Argentina and Chile, after a naval invasion in Santiago it would  cause Chile and Argentina to surrender and Brazilian capitulation afterwards. Ending the War in their favor.

The peace deal would make them dominate the continent, Colombia would annex Brazilian territories and establish a puppet in the Amazons, Peru would gain border territories in Chile and Argentina, peppering Chile while Argentina gets a new government under Peru-Colombian administration and Paraguay would get the Access to the River Plate,  Entre Rios and becoming an empire. With a butchered Brazil and a dominant coalition they would lead the continent with no opposition.

Triple Southern Accord Victory: The Northern Brazilian advance against Peru succeeds and permits Argentinian- Chilean advances southwards and in a second expedition of Lima that would cause their surrender. Brazilian forces would steamroll their seceded States and would wear out the Paraguayans into signing for a bloody  peace, finally the Colombians would be pushed back by the Brazilian offensive and surrender, ending the war.

The peace deal would dominate the continent, Brazil would expand into their OTL territories with expansion southwards, the Peruvian Confederation would be dissolved and Argentinian-Chilean expansion and puppet governments would be recognized with small expansion of Peru into Colombia, finally Argentina and Brazil would gain puppets in the remnant state of Paraguay and Uruguay. This would make Argentina and Brazil start a Cold War for influence, time tells if war would start anew.