Different companies isn't really a problem; there were at least a dozen or so big US railways during their golden age (off the top of my head, the Union Pacific, the Central Pacific, the ATSF, the New York Central, the Southern Pacific, the Norfolk and Western, the Pennsylvania Railroad, the Great Northern, and there are a lot more that I don't remember), and our rail system is just fine (for freight). Argentina is smaller than the US, obviously, but it could probably support a half-dozen to dozen railroad companies in its heyday, with fewer as newer transportation options intrude.
Different gauges, however, is a big problem. Makes transshipment really hard. So figuring some way for them to standardize relatively early (ideally, considering the thread challenge, on 1435 mm) would be helpful.
EDIT: Also, I love how your map goes out of its way to say that it's only depicting effective national boundaries, and shouldn't be taken as a statement that those boundaries are indeed correct...