There were several revolts that could easily have led to the breakaway of particular areas of Brazil. State formation in Latin America in the early-mid 19th century was complicated business, and the question of what states would exist, and where their borders would be drawn was not settled until the resolution of dozens of rebellions, invasions, foreign interventions and regional wars.

I really only know anything about one: The Guerra dos Farrapos (the Ragamuffin war, though I have yet to hear anyone actually call it that) as it borders on Uruguay. The conflicts in the two countries are not entirely separate, with a porous, disputed, notional border and frequent cross-regional alliances of political parties and caudillos. Gauchos in Rio Grande do Sul rose up in 1835 against the provincial governor, and declared independence, leading to a protracted conflict to reclaim the state. They succeeded at first, taking Porto Alegre and establishing an independent state (the Republica do Piratini) in Rio Grande do Sul, and another in Santa Catarina, the short-lived Republica Juliana. The war continued until 1845, with the central government being distracted by other rebellions, and attempts to sue for peace frustrated by the problem of slavery (the rebels wanted freedom for the slaves they had freed, and the Brazilian government was obviously opposed). But eventually the central government regrouped, reorganized its army and tipped the balance of power. The treaty of Ponche Verde was signed, with fairly generous terms for the rebels, but also de facto incorporation back into the Brazilian state.

They rebels were supported by Fructuoso Rivera in Uruguay, who was the military leader of the countryside, and his Colorado faction was engaging in its own revolt against the Blanco government of Manuel Oribe in Montevideo. Rivera had been recently driven out of Uruguay by Argentine and Blanco forces, and so he sought allies in Rio Grande do Sul. He provided support to the rebels in exchange for their supporting his own position in Uruguay.

This was made even more complex by the presence of Giuseppe Garibaldi and his small legion of Italian liberal adventurers/soldiers of fortune/pirates, who would later shift their operations to Uruguay during their civil war before returning to Italy in 1848 to join the revolution there. Not to say that Garibaldi was somehow decisive, but it is certainly notable not only as a chapter in his life, but also in terms of the presence of Europeans of many nationalities fighting in these conflicts.

Rebellion in Rio Grande do Sul didn't entirely end until the 20th century; the Saravia/Saraiva brothers Aparicio and Gumercindo led a series of rebellions on both sides of the border in support of greater federalism and against the encroaching centralism of their respective national governments. Neither succeeded, but this was as late as 1895, so armed insurgency against the Brazilian government on the southern border did not stop until at least then.

The whole mess is illustrative of the way in which national and political causes in the region were fluid. Participation was certainly not limited to local interests, with adventurers, mercenaries, recent migrants, adjacent warlords, European powers, and anyone else who wanted a piece of the action joining in at various points.