If Portal 3 ever comes out, what would you want the story to be about?

Portal is one of, if not my favorite video game series. I love the challenge level, I love the humor and story, and I love the characters, especially the main three: GLaDOS, Cave Johnson, and most of all Wheatley. (I mean, yes, Chell is the main character, but given her mute status, she doesn't have a whole lot of personality aside from just being the player's avatar). I would absolutely love to see a Portal 3 some day! That being said, I have no idea what the story would be about.

The main issue I think the game would have is the worry of retreading old ground. In my opinion, the one character you cannot make a Portal game without is GLaDOS (unless it's a fan mod like Portal Stories: Mel, and even that found a way to work her in the story even if she never appeared). Canonically, right now, GLaDOS is out of human test subjects after she killed thousands to get rid of a bird, but I'm assuming the single player campaign would still have a human protagonist. I just don't know if that would be Chell. Chell got the happy ending she deserved, and while people have speculated that Chell didn't actually get released from the facility, I personally don't think GLaDOS was bluffing when she let her go. And if Chell really did get released, I can't see any reason Chell would come back to Aperture unless Portal 3 is just a video game adaptation of Blue Sky, which is doubtful. But at the same time, Chell and GLaDOS have such a fun rapport at this point that I don't really want her to be replaced.

Another character that I don't really see returning apart from maybe a cameo is Wheatley. I could see him cameoing, as Aperture is crazy enough to invent Wi-Fi that works from space, and would allow him to essentially Skype the facility for a time, but I can't really see him actually returning from space. The only ways I could think of him coming back is through a player-led rescue mission (which logically wouldn't work, as even if the player portals onto the moon again, Wheatley would've floated much farther away at this point) or a plot contrivance (like how he appeared in the Lego Dimensions extra Portal 2 level). So, as much as I would love to hear more Wheatley dialogue, I just don't think he would come back.

I don't really have an answer to this question, as I have no idea what I would want the game to be about other than it would need to have GLaDOS still. Gameplay-wise, I would be really interested to see what new puzzle mechanics Valve could come up with. It might be cool if a portion of the game replace the Portal Gun with a different device to help you through the test. Granted, I wouldn't want this the whole game, but maybe for a chapter or two, it would be neat to use something different. And there's certainly a market for it, with two of the mods made available on Steam (Aperture Tag and Thinking With Time Machine) do just this. AP gives the player a paint gun, which shoots out the blue and orange gels rather than portals, while TWTM gives players control of a time machine, which essentially clones you for a short period of time with your previous movements to allow you to co-op with yourself.

So the questions I have are: Would GLaDOS be testing Chell this time or someone new? Would Cave Johnson make a return appearance in any way? (Probably.) How long after Portal 2 would it take place? Would the story remain confined to the facility or would we finally delve into the outside world? And what new puzzle mechanics could be implemented in this game?