For Fidelity this user found a way here....
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.
Unable to import second instance of brokerage (completely different accounts/credentials/data)
