I'm Portuguese and also lived in other countries in Europe and Multibanco is a vastly superior system to everything else I've seen, but on the ATM side rather than the payments side (everybody seems to have their own payment solution or, like the UK, rely on the likes of Visa and MasterCard) - already back in the 90s in Portuguese ATMs, in addition to withdrawing money, you could check your bank account balance, get a statement with the last transactions on your account and even pay your bills all this well before widespread internet access and online banking: that stuff was way ahead of its time back then.
Right now they've added stuff like touchless mobile payments and transfers, but the rest has caught up with them so you'll find such solutions in most countries plus that whole system is entirely local as it's the product of ages ago (before neoliberalism) the government forcing the banks to get together and create a company - SIBS - under shared ownership of the banks, responsible for setting up and managing a national interbank payment systems.
I wouod even say that the Multibanco system probably helps Portuguese banks maintain market lock-in against external competitors, which does get translated to Portugal having pretty high banking fees compared to the rest of Europe, especially for one of the poorest countries in the EU.