Can much of southern Latin America be united as one for good?

If a strongman takes over I think Gran Columbia would turn into South America's Yugoslavia in that it Will only be united for as long as the local Tito is alive. A few years after he dies the country Will collapse into civil war due to internal differences.

One of the most natural ways for South America to lessen its post-independence fragmentation is allow the old Spanish Viceroyalties to keep their unity during and after the independence process. Their division in the OTL states was by no means inevitable nor necessary.

The breakdown of Gran Colombia might have been prevented by lessening the destructive conflict between centralizers and federalists, either by enabling a faction to reap a decisive victory or by achieving a functional compromise between them. Also reducing the personal rivalries between a few key members of the leadership that became rallying points for these factions (e.g. by removing a few of them with timely deaths) would have helped.

Much the same way, if the civil wars between centralizers and federalists can be toned down during the formative period of Argentina, the new state would be much more likely to get the upper hand with some luck in the Cisplatine War with Brazil and keep control of the entire Rio de La Plata region, including Uruguay and Southern Brazil. In addition to considerably increasing the resources of the federation, this expansion shall reduce the dualism between Buenos Aires and the interior provinces that was another serious source of instability for early Argentina by providing Montevideo as an alternative coastal hub. If this can be accomplished, Greater Argentina should have relatively little difficulty absorbing Paraguay as well.

Greater unity of the Andes region can be ensured by letting Peru and Bolivia coalesce in one state. The easiest way to let it happen seems a success of the Peru-Bolivia Confederation, say because Argentina stays neutral and Chile gets defeated in the War of the Confederation.

If all of this can be accomplished, South America can be consolidated in four large states: Gran Colombia, Peru-Bolivia, Brazil, and Greater Argentina. Once they are stabilized, these states are basically going to encompass natural geopolitical and economic cores with no serious separatist issues. Chile is kind of a peripheral outlier in this regard due to its peculiar geography, but nonetheless there should be enough ground to let it be absorbed either by Argentina or Peru-Bolivia, say because it loses a war with either power.