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As another commenter mentioned, for the EU many fintechs will opt to get a banking license in Lithuania.

For example, Revolut is a bank in the EU via a Lithuanian banking license, but only an "e-money institution" in the UK (though the application to become a British bank -- and for that matter, an American bank, and other jurisdictions -- is in progress).

Monzo is a UK bank, but opted to cancel their US banking application, and I don't believe is an EU bank either (someone please fact check me here!)

I don’t know of any that will extend credit across the whole EU.

The closest service I have gotten to this was (also not exactly an EU company) American Express - but that was still two different legal entities.

A lot of Fintechs get their banking license in Lithuania now for the EU