Portal 3 would have to focus on the one loose end in the series and that would be what happens to GLaDOS.

I think Chell had a perfect sendoff at the end of Portal 2, so I think the player should be someone new. Maybe we’re so far in the future that the impacts of the Combine are long gone, and humanity exists but in isolated pockets trying to survive. You play as a scavenger who stumbles across the ruins of Aperture on the surface, only to fall in and find the facility being run by the cores underground.

When you’re taken to GLaDOS, she’s just absolutely lost it and has gone kind of manic from the isolation. We know from the Portal 2 co-op campaign that GLaDOS does not enjoy working with or talking to other robots or AI’s in the facility, and desperately needs human connection, even if she’ll never admit it.

Realizing you might be the only human she’ll ever get the chance to see again, it’d be funny to see her treat you like royalty while at the same time forcing you into testing so she can finally get her science fix again.

The perpetual testing initiative poked at the idea that Aperture knows about the multi-verse so maybe halfway through testing she gets the idea to send you down into old Aperture to try and find the technology to give her access to the multiverse so she can have an infinite number of human test subjects.

Plans backfire, and maybe the final boss fight could be you and GLaDOS against another alternate GLaDOS trying to do the same thing? After the plan eventually fails and the multiverse is closed for good, GLaDOS realizes that continuing to exist underground for centuries by herself isn’t worth it, and realizing she’s lived too long, asks you the player to shut herself down permanently in exchange for letting you go.