Certainly. Some of the most prominent figures of the independence wars, including Manuel Belgramo and San Martín, were quite in favour of a monarchy. San Martín himself was supported by many as either a king of Peru or Argentine, though he refused such offers.
Belgramo seems to have originally hoped for retaining at least some ties with Spain, hoping that a member of the Spanish royal family could be a king of independant Argentine, a proposal immediatly rejected in Madrid.
There was also the Inca plan, which is frankly a somewhat ridiculously sounding idea, of creating a united monarchy of Peru and Argentine, under an Inca nobleman. The idea found quite a lot of support in Peru, but it was disliked by Buenos Aires, as it would move the centre of power quite northwards. Also, after a brief wiki search, it seems that the Argentinian counter-proposal was a Buenos Aires centered monarchy under a member of the Spanish royal family, then living in Brazil, who was however convinced to refuse by relatives. They then switched to supporting a French aristocrat (trying for the Duke of Orleans), and then the prince of Lucca! Mostly because the strongman in Argentine disliked the idea of a ruling Inca. When these proposals failed (often due to refusal of the possible monarchs) only then were republics enacted.
So yeah, with some better luck for the monarchists, South America could have been full of monarchies. Though whether they would stand the test of time is a whole another thing. Hell, perhaps a Peru based Inca monarchy could have been created, if the locals broke with Buenos Aires early on