I've been thinking as of late that once the Anglo-Spanish wars of approx. 1807-1812 in/around present-day Argentina are over, Salta/Jujuy becomes part of what would become Bolivia (because the British lose there as well as in OTL Bolivia). At the same time, Cordoba/La Rioja, the Cuyo, and Tucuman/Catamarca/Santiago del Estero (or greater Tucuman) all become either Spanish-speaking republics with varying degrees of British suzerainty (cf. the Boer republics in South Africa) or British protectorates. Cordoba becomes a British colony soon afterwards because British settlers are interested in settling some areas there, and La Rioja is transferred to either greater Tucuman or to the Cuyo. Both the Cuyo and greater Tucuman remain republics or protectorates (and may - just may - become British colonies for short amounts of time, again like the Boer republics). Eventually, after these two areas attract some British settlers - e.g. because of a boom in, say, wine or tobacco (the main products of the Cuyo and Tucuman, respectively) - they form the Argentine federation ca. 1875-1880 together with Cordoba and with descendant British colonies in the area formerly covered by the River Plate Colony (occupying the area of the Intendency of Buenos Aires and Government of Montevideo as they were from 1783 to 1806).
Meanwhile, Paraguay falls within a few years of the original British invasions of the River Plate to a joint Anglo-Portuguese force (despite the fact that both the British to the south and the Portuguese to the north and east are Paraguayan enemies). This is because Paraguay, from the time of a British takeover of the River Plate, is completely cut off from the rest of the Spanish Empire and is surrounded by the British and Portuguese, and also the Chaco to the west (with its harsh environment and hostile native peoples). The British and Portuguese, once they start occupying Paraguay, support a junta for independence from the Spanish, and Paraguay becomes effectively independent. Because Francia emerges as the leader, however, the British try successfully to overthrow him, with his very isolationist tendencies, since the British want to trade and to provide security for the region. Paraguay then becomes either a British protectorate or a joint British-Portuguese (and then British-Brazilian) protectorate for a long while - kind of like Anglo-Egyptian Sudan. It refuses to join the Argentine federation, and it ultimately gains full independence, I'm thinking in 1954. All this time, Guarani is one of the main languages, existing alongside English and Spanish (and possibly Portuguese too) - kind of like the Philippines. The British also don't allow Solano Lopez to be the leader in the 1860s for fears of regional instability, and the Paraguayan War is thereby thwarted (or at least reduced).
In the 1870s, the British take over much of the Chaco (much like the Argentines did OTL), up until the Monte Lindo River (slightly north of the OTL Argentine-Paraguayan border), and the Bolivians take over the rest of the Chaco. For the first few years, there is a dispute between the British and the Bolivians over the area between the Monte Lindo and Verde Rivers, but that is ultimately arbitrated in favour of Bolivia. The British also take over Misiones (again just like the Argentines did OTL) and the Brazilians annex some lands to Paraguay's north/east like OTL.