Its an interesting example, subways seem to have some minor room for competition, so the argument against privatization based on "there cannot be competition" does not quite apply.
Even here though, there is a coordination problem to ensure various companies remain mutually compatible.
Competition on public transport is limited by the fact that you often need a cohesive network to get from A to B via C & D. If multiple companies cooperate on crossover ticketing and align their schedules, yes, it can work. Even more likely to work is a model where a central authority opens tenders for specific services, and transport companies can compete on that.
Then again, I don't think it's viable to build subway tracks and tunnels to compete. Even if you have space under the earth, there may not be space for more stations, and good station locations are important too.
Even here though, there is a coordination problem to ensure various companies remain mutually compatible.