Of course you can have multiple companies competing on the same rail. That's how it's done elsewhere. Profit and public service are not mutually exclusive. Indeed profit is the *symptom* of serving the public well. It's the political pressure to be an employer of last resort that has always been PRASA's biggest problem, not the ticket price subsidy. You could (and probably would) continue to grant a subsidy to a private PRASA. 

You want the "right people" to be running this "public service". This is the Left's never-ending nightmare, because it turns out you just can't reliably get the "right people" unless you have the right ownership structure. Yet if you have the right ownership structure, the right people are all but guaranteed. Take a look at Telkom's turnaround.