Game style:
Gun-based TPP platformer, with possible FPP mode to turn on. Like in Sonic Adventure games, each character should have a bit different style of game and different levels, but they all are connected with the story.

Platform:
PC. Maybe consoles also, but PC should be the root.

Time period:
Sequel, for the sake of more characters and a closer look to ones like Lori.

Graphics type:
Cartoony, but without cell-shading. I'm sick of cell-shading already.

Multiplayer modes:
Obviously, as much as possible.

Other companies involved:
Whoever worked on Ratchet & Clank.

Cinematics:
Heavily story based. There's nothing better than a good story. And that doesn't have to mean stopping the game each 5 minutes for another cut-scene.

And I'd also like to add:
-multiple gun modes, like in Unreal
-fighting even hordes of enemies, like in Serious Sam (but platformer-style)
-characters' comments on the action, like in Duke Nukem 3D
-each gun has it's own look, and NOT ALL IN ONE BLASTER
-a level editor, of course
-leave it with the mod music support
-team levels, where you meet one of other characters and he helps you out; that should be rare or maybe even hidden
-secrets unlocking secret levels and hidden stuff, including easter eggs!