At the end of the first game they're going to rescue Lili's kidnapped father! I think this would be a terrific storyline to follow up--you'd get to see a lot more of Lili, for one thing, and learn about the Psychonauts as a whole--maybe it could take place in the main Psychonaut HQ! That would be all kinds of cool.
I also think it would be cool to have a multiplayer version--maybe an add-on or unlockable thing--where a couple of people could play Sasha and Milla. Team fighting is not something we got a lot of in the original. Sasha would probably have great Psi Blast skills, and Milla would be able to Levitate for much longer than a regular Psychonaut? I hope we'd get to see more of Sasha and Milla's pseudo-relationship, too.
New skills you could learn from the other Psychonauts at HQ--I like the idea of hydrokinesis, parting the water! Maybe the Psychonaut who gives it to you could be called Moses (
) and have a watery mind that requires a ****-tonne of platforming until you get the ability. Maybe a surfing based mind?
Ford's mind - I could see it being organized into a bunch of different sections with the various personas, and with the real Cruller in the very centre, hidden away--maybe Raz would be able to sort out Cruller's shattered psyche? Maybe too it could include something to do with that very sexy female voice in the tree-trunk underground transporter thing? Like...his former sexy sidekick and secret love who was killed in the line of duty or something. Or maybe she still works at HQ and there can be complex drama! A skill to get from Ford would be teleportation--we know he can do it from the original, and it would be a good one to incorporate into other essential gameplay. Instead of teleport worms have glowing blue buttons you can save to teleport back to--but you can only save 3 locations at a time, maybe?
Lili's mind - I don't know what would be here, probably something (once again) to do with her father, since he is the head of the Psychonauts! Maybe she feels she has a lot to live up to, and is rebelling, maybe she needs to reconcile with her dad just like Raz. This mind should be near the end, and be a key to get to her dad.
Raz's dad's mind - Can you imagine? It would probably have memories of the gypsy psychics that killed his father, as well as his circus and acrobatics memories. And more of Raz's mother?
An OCD mind would be *fantastic* like someone suggested previously, as would a cyborg mind--it might look like the matrix, all moving, green, zeroes and ones.
How about the mind of a yogic master? A super-calm, organic place, but with magma under the surface. Maybe Lili's mom is into yoga and meditation? Maybe it's just another Psychonaut who can teach Raz a "Meditation" skill at the end that will give him back health? There would be complications with this, of course, since it could make the game much too easy early on and without the right restrictions, but still!
What about a horror movie mind? Werewolves, zombies, and vampires are all paranormal like psychics, it would be an interesting fit. Maybe Raz could learn Alchemy and turn the things he has to kill the werewolves with into gold/silver, etc.?
Other skills Raz could learn in addition to the ones he already has: Teleportation, hydrokinesis, meditation, alchemy,like I mentioned above, but also telepathy (used to get key information out of the minds of people at HQ, since this is no longer a training facility, and there won't always be someone to give you information straight up, but it could also be used for mind control on weaker-minded individuals like...grounds crew or something at HQ), and precognition: since Raz is already a gypsy, this is a natural fit.
You could even get more into the pseudoscience realm and explore the two realms of psychic powers: psi-kappa and psi-gamma (one is action-based, the other is strictly cognitive, or passive). With that cyborg mind? Psionics! Maybe there Raz could learn Electrokinesis there, but I think it would be pretty close to the Psi-blast, unless he had to draw it from electronics or power outlets nearby. (Although that is fringing on an Okami ripoff.)
You could EVEN go all Freudian or Jungian and have a mind full of archetypes (for Jung) and one full of sexual repression (Freud). Maybe?
Oh man, I hope there is a sequel.