Have the users only open one file. Hide the others but host them.
Put navigation buttons on a 'menu' layout where they select the file that they want to access by clicking/tapping it. Have those buttons use open file to open the other file.
As long as the files have matching account names for your externally authenticated accounts, they won't get an additional password dialog.
This is probably more related to the FMS setting to only list files that the users have an account in. That would account for the two logins.
If the deployment is all windows then the Pro users can benefit from SSO to avoid this. Go users and Mac FMP users can't use SSO.