It would have to be a new account at a different bank. FDIC coverage is per bank, per depositor, and per ownership category (e.g. single vs joint account).
i'm pretty sure you're wrong about that, but not invested enough to check.
but if you're right, it seems a little silly, why impose that "diversification" on bank customers? if 100 millionaires live in a city, why should they all have accounts at all the different banks, as if that's somehow safer for the FDIC than have the same funds spread around in the same quantities across the same banks, just under different names.