Can one buy additional insurance for money in a bank?

No . . . the. “insurance” is a guarantee by the US government to cover losses because a bank fails.
Just spread your bank accounts to several different banks, if you have more than $250,000.

Or in multiple ownership categories at the same bank

Some brokerage accounts offer guaranteed protection of accounts up to much higher amounts. When the crash occurs to wipe out those guarantees, then a guarantee wouldn’t have mattered, anyway.

No independent insurance company is going to write insurance policies for money in bank.

Putting aside the FDIC (or the Canadian equivalent thereof) you have to look at how insurance companies operate.

- they pool together people who have similar property (or health issues, or whatever) and do some actuarial work about how many of those people will possibly have a loss during that year.

- based on the likelihood of loss, they charge premiums that will (collectively) cover the potential loss.

- they invest the money until people make claims.

So now look at who the clientele for extra insurance might be. People who already have more than $250,000 in a bank. How many of these people will want to buy extra insurance? (Because remember, it is the pool of money that clients pay that is actually what is paid out in insurance claims).

My guess is that the number of people who would want to purchase this extra insurance is ZERO. There’s no market for it. There are enough ways to spread one’s money in different banks (spreading the risk) or different accounts, that no one would buy it.

My Uncle Guido can provide a policy that you can’t refuse.