Any coalition of banks can. Replacing Visa is a daunting task, but rolling out PoS support and the technical challenges are peanuts compared to actually getting banks onboard. Visa itself was started by a single bank, and Mastercard was started by a coalition of banks. They can do it again.
Interac[1] is Canada's debit system, originally created as a non-profit by our largest banks way back in '84, and these days is supported everywhere. The large banks are already used to bullying their way through political or bureaucratic challenges, and a single Canadian bank typically has trillion(s) in managed assets - they _can_ bully Visa.
Zelle[2] (2016) is a limited (etransfer only) clone for the American market, UPI (2016) in India, UnionPay (2002) in China, carte Bleue (1967) in France, etc etc. What's missing is cooperation between national systems like these, as well as lending as they typically only do debit instead of credit.
Any cooperation between these systems would likely get spun out as a separate entity, which would eventually just turn into a new Visa or Mastercard - but 3 choices is better than 2.
[1]: https://en.wikipedia.org/wiki/Interac [2]: https://en.wikipedia.org/wiki/Zelle [3] https://en.wikipedia.org/wiki/Unified_Payments_Interface
Zelle won't become that. Zelle was designed to offload liability onto consumers using the carrot of instant transfers.