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i.e. two Discover It's?
I have 2 US Bank Cash+ Visa Signature cards.
All of the big banks will allow you to have multiple cards that are of the same type; the same may not be true for smaller ones or credit unions. From what it seems, Disocver is really strict about someone having mroe than one of their cards. You can try, but usually it will come back saying you already have the card.