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Other than those primarily involved in the banking business?
I know Target has their own bank, I know H&R Block does too. Discover and AMEX do of course but that's kind of their primary business moreso than the processing business so not sure if I'd count that.
Others in non-banking industry that own banks?
What do you mean by "Own their own banks." Because Amex offers HYS accounts, discover offers MMA, HYS and CDs.
Target on the other hand just does the financing on their own cards, and isn't so much a "bank" by the literal definition.