If you haven't seen it, you should.  It's probably the bast Pixar movie they made.

I was wanting to make an RP in that world where the Bureau of Superhuman Affairs (what I call the group that helped the supers hide, as they didn't say in the movie) is trying to bring back the Supers.  They convinced several teenagers and young adults that were Supers to become Heroes and put them up in rooms in an apartment building, one room for the guys, another for the girls.  Frozone, who owns the building and lives in the penthouse, trains them, with the Incredibles coming by occasionally to help out.  Tomorrow you'll go on your first patrol, but tonight you'll have your most difficult and dangerous mission yet: babysitting Jack-Jack.  (Depending on how well it goes, I may spring something serious on you halfway through.)

A few specifics of this universe:

[hider=NPCs I know I'll use]
Robert "Bob" Parr (42)- Mr. Incredible (Super Strength, Durability)
Helen Parr (40) - Elastigirl (Elasticity)
Dashel "Dash" Robert Parr (14) - "Jet" (Super speed)
Violet Parr (17)- "Invisigirl" (Invisibility, project forcefields)
Jack "Jack-Jack" Parr (Almost 4) - (Demon form (Super strength and agility)
Lucius Best (40) - Frozone (Ice)
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[hider=Super power rules]
1) Super abilities usually manifest shortly after you are born, though they can manifest as a result of exposure to radiation, toxins, or other forms of danger.
2) When abilities first manifest any super-human genes you have (genes that are beneficial mutations compared to your normal DNA) will activate and deactivate, seemingly randomly, until you either reject them completely or accept and consciously use one combination.  Those genes will then lock on, usually combining into one power.  For example: Bob Parr has super strength and Zero-range Telekinesis.  Helen Parr has super agility, shapeshifting, and minor reality warping abilities.  Dash has his father's Zero-range TK and his mother's agility, letting him move at superhuman speeds without injuring himself and withstand the forces of it.  Violet got her father's Zero-range TK and her mother's reality warping, giving her the ability to create forcefields and bend light.  Jack-jack first manifested his mother's reality warping, letting him phase through solid objects, but after syndrome captured him the genes for shapeshifting activated, then, when they didn't let him escape, the reality warping deactivated, but his father's super strength gene and his mother's super agility genes activated, letting him take his demon form.  Because of the success of that combination, he accepted it and it became his permanent power.
[/hider]

[hider=What's happened since the movie]
1) Syndrome's body was never found.  Some think the jet engine pureed him, then the explosion destroyed what was left, and some think he used his "zero point energy" tech to shield himself and survive.
2) The Supers are public again, but few of them remain.  Jet and Invisigirl have had to go on patrol on occasion to help out.
3) Besides the few that survived, there are also children from the old supers, including ones the Supers themselves didn't know about, and non-hero supers that decided to come out of hiding after the "Syndrome" incident in Central City.
[/hider]