Portal 2 doesn't need a sequel, and I wouldn't even want a Portal 3.
Making a sequel that's able to compete with the nearly perfect original Portal was already a nearly impossible task as the game's writers discussed during 2012's Game Developer's Conference. And chances are, Valve still has no plans to jump directly into another Portal sequel. But just because I don't want to see a Portal 3, that doesn't mean I don't want to see more from the Portal universe.
The magic of Portal hasn't ended completely yet anyway. Fan-made mods aren't held to the same standards as the in-canon adventure, so even if they might not be quite as good, you can escape into Portal's world by either further exploring the game's fan fiction or facing even more ridiculous puzzle challenges.
The time travel hinted at in a portion of Portal 2 has been covered through a mod called Thinking with Time Machine [sic]. Other fans made a prequel that sets up the events of GlaDOS' creation in Portal: Prelude. And the Portal 2 map editor pretty much ensures that any time I just want to flex my brain against challenges that surpass even Valve's creation, I can find a map to play.
Of course, things have been kept vague enough in Portal's story that Valve could always potentially return to the game and its characters. GlaDOS is still alive. The main character Chell is somewhere out free in an unfamiliar world. And we have no reliable way of knowing how much time actually passed between the events of Portal 1 and Portal 2. Another Portal game could take place pretty much anytime, including well after the culmination of the Half-Life series.
Aperture Science in Portal and the Black Mesa facility in Half-life have already been explicitly linked in both series. And having Chell explore the world long after the events of the alien Combine invasion from Half-Life 2 could provide an interesting narrative way to bridge the gap between the two franchises and give us insight into what happened after Half-Life 2: Episode Two.
But could that be called a Portal game? Portal is more about combining comedy and puzzles, in contrast to the seriousness and shooting gameplay of Half-Life's world. Any time spent exploring the world outside the facility makes the "Portal" moniker sound out-of-place. I think we're still going to see GlaDOS, Chell, and the portal gun, but as cameos in a Half-Life game proper.
Those wonderful toys?
The portal gun is such a clever tool, and while it has obvious limitations on what types of surfaces can be used to make its dimensional portals, creating short chapters that use the technology in a limited way makes more sense at this point than trying to craft another entire game around the tech. And that's where I'd most like to see the continuation of the main Portal story extend anyway.
While Half-Life's Gordon Freeman probably wouldn't run through a full Aperture testing lab with the gun, it's possible that more of the devices exist somewhere in the world, and who better to explain the device than Chell?
In Portal's conception as the game Narbacular Drop, it may not have been originally intended to fit into the Half-Life universe, but the two series are inextricably linked, and I'd liked to see that connection extended even further. Trying to make a full Portal 3 in the same testing facility with yet another battle against rogue AI, it would be almost impossible to capture the same sense of newness and surprise that made the previous games so good.
A handheld Aperture Science Testing Device
So how could GlaDOS and the testing chambers continue without overreach into the Half-Life lore or just rehashing similar stories and ideas? The answer's simple: A mobile game.
Portal has always been more about the puzzles and humor than anything else, and I'd rather any efforts towards a full 3D release go towards Half-Life. But there's always room in my life for a great mobile puzzle game, and that's something Valve could easily fit into the Portal universe.
Hitman GO, a recent mobile title with a board game aesthetic, provides an excellent example of staying true to the feel of a series' source material while simultaneously taking the gameplay in a completely different direction. And what is GlaDOS' ultimate goal if not to pit able-minded test subjects against one another in a set of grueling mental trials?
Portal's iconic turrets would fit perfectly into a standalone mobile outing. And at the end of Portal 2, they had even created their own form of civilization--singing an operatic farewell to Chell. Slides in the science facility revealed a massive Animal King turret that's able to command the worship and fear of entire governments, who would make a great comic character to expand on through short games.
Valve isn't known for making mobile games, but neither was Blizzard, a company that recently spun off their popular Hearthstone game to mobile. Fan reaction to a mobile Portal game would be initially negative, but I think it'd be possible to make a really great, novel experience that way that doesn't have to be called Portal 3.
But then again, given how effectively Blizzard is able to siphon money out of my wallet through Hearthstone and how Valve empties my accounts through their regular Steam sales, maybe I shouldn't give them more ideas on how to make me go broke.