Set it in a partly open world
Mirror's Edge stars Faith, a courier who delivers physical documents between people who don't want their communications monitored by the totalitarian government. It was disappointing to play the game and then find that experience instantly take a backseat to a short, scripted singleplayer story.
But only sections of it should be open, like hub worlds that connect more constrained missions. Mirror's Edge offered plenty in its scripted areas that's worth bringing back, like the puzzle-platforming atriums that challenged you to scale the innards of some enormous structure.
Add destructible buildings
Freerunning is about gaining a sense of ownership over an environment by traversing it in unexpected ways. (Sometimes it's about running along a small wall while your audience waits for you to reach the next impressive bit). The first game did a great job of that when you were up on the city's rooftops, and a less good job of it when you were inside, trying to quickly maneuver through office space.
Make it a stealth game
Mirror's Edge's combat was certainly interesting. It was based around close-combat melee. You could only get guns by stealing them from the hands of an enemy. They significantly limited your speed and agility, and when they ran out of ammo, your only option was to toss them on the ground.
Don't change too much, please
Mirror's Edge didn't sell as well as EA hoped, which is why five years have elapsed since the original game. I don't care. Mirror's Edge is one of the most interesting and brave games of the past ten years. There are reasons why people have been calling for a sequel all this time. There are reasons why it's the first game I install on every new PC. There are reasons why even its flaws only serve to make its fans more protective of it.
