BoA offers 5.02% via their "Preferred Deposit" offering:

https://olui2.fs.ml.com/Publish/Content/application/pdf/GWMO...

But you have to start with $100k. (You can decrease that to as low as $1 anytime after though).

Ally and Interactive Brokers both offer those rates, and they are in the $5-9 billion market cap range. Not sure if they qualify as too big to fail.

Wealthfront has high percentages right now.

Wealthfront is not a bank, they use a bunch of small banks: https://www.wealthfront.com/cash-account-participant-banks

Amex is at 4.3 now