I'm trying to avoid the need for users to sign in twice: is it possible to use third-party authentication and then check against a session variable to automatically sign a user into MRBS?

I already have an external database that I am successfully using to authenticate within MRBS, but I use that same database to authenticate for several other applications (MRBS is the only one that requires a second login).  I would love to unify them.

For example, John Smith has username john.smith and successfully logs into the non-MRBS system.  $_SESSION['username'] is set to "john.smith".  When he goes to MRBS, I want to be able to check for the username session variable and if it's set, check the value (john.smith) and log him in automatically.

I feel like this is probably easy to do, but I can't figure it out and thought it would probably be best to just ask.  Any help would be appreciated!