See this post the user figured out how to import another account from Fidelity. Maybe it will help for other banks.
https://ttlc.intuit.com/community/tax-credits-deductions/discussion/unable-to-import-second-instance...
User said.......
After I had downloaded from one account and the second one would not work, I looked at the Fidelity website and noticed that I was already logged in to my account (the one I had downloaded from). Turns out that TurboTax had not dropped the connection from the first account. I logged out of that one and tried to download the second account and I was presented with the login screen and could then download from the second account.
