A potential sketch of alternate events along these lines:
-Spain after Columbus' first return voyage refuses to seek or accept papal arbitration about dividing global spheres of influence with Portugal
-In retaliation, Portugal competes more in America, at least after the discovery of Brazil, the focus of Portuguese exploration around Brazil moves more to the north and west faster
-Ultimately, Spain gets to all the greater Antilles, Mexico and Panama first. Portugal gets to Aruba, Curacao and the northern coast of OTL Colombia and Venezuela first
-In the 1500s a Portuguese rather than Spanish expedition conquers the Inca.
-even if struggling from time to time makes Panama and northern Colombia trade hands a couple times, the long-term trend is Portugal dominates South America.
-The earliest prime focus of Portuguese South America is some sugar plantations and prospecting operations in Venezuela and Colombia, and then conquered Peru.
-Before the 1500s are out, sugar planting in northeast Brazil becomes another Portuguese focus on the continent. A Portuguese explorer follows the Amazon downriver from Peru, like OTL's Orellana.
-By 1600 Portuguese mapping and claiming of South America (but not actual occupation/settlement) is fairly complete. The TL's flipping of Peruvian wealth out of Spain's hands and into Portugal's has knock on effects for their economies and power, diminishing Spain a bit and boosting Portugal. Even if there is an Iberian Union, the Spanish North America, Portuguese South America divide persists over the long-term.
-Portugal continues to do everything it did in Africa, the Indian Ocean and Far East in OTL.
-With Portuguese forts and trading posts in Africa, the use of African slaves for the mines of Peru is greater than OTL (although, even under Spain, this was a significant thing). Long-term there are more Afro-Peruvians than OTL.
-By the early 1600s the Dutch and English begin to poach on Portuguese American territory. In this ATL, with the Portuguese more extended throughout South America, and having Peru as their #1 point to defend, lose northeastern Brazil and the lower Amazon to the Dutch permanently. Northern Brazil ends up as an enlarged version of the Guianas, with Netherlands, Britain and France running sugar colonies. Portugal retains Venezuela-Colombia as part of the forward defense of Peru.
-Nevertheless, the Dutch competition in particular motivates increased Portuguese efforts to settle and control whatever it can of South America.
-In the 1700s massive Portuguese migration goes all over their South American colonies. The frontier spreads southward to incorporate the southern cone, Chile, Argentina and southern Brazil.
-Conceivably, except for the Mega-Guiana/Amazonas/Recife area, the rest of South America becomes independent as a single enormous and diversely endowed empire.
-things get even more different as time goes on.