If you put that kind of money in a savings account, the bank will call you twice a day until they have made you move the money into something more profitable (for them.)
If you've got more than $250K, I'd split it up into multiple accounts at different banks.
I think you're mistaken about the first part of your statement:
The FDIC says, "All single accounts owned by the same person at the same bank are added together and insured up to $250,000." (see https://www.fdic.gov/deposit/covered/categories.html )
But you are correct that it can be doubled, tripled, quadrupled, or even greater by opening different account types such as a Retirement Account, a Joint Account, a Revocable Trust Account, etc., at the same bank since each account type seems to get separate treatment (according to the same FDIC link).