Many financial institutions will issue credit cards to individuals who have no other relationships. Most people have between 3-5 credit cards, but usually 1 deposit and 1 investment account.
There is no federal or state law prohibiting it, only your credit policy, and potentially documents. Before you close the account, you may want to verify that the bank is allowed to close it for an account not in default.
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Integrity. With it, nothing else matters. Without it, nothing else matters.