I figure a good way to make the PPG separate characters would be to split up the powers a little bit, but in a way that still more or less makes sense.
Blossom: Mage. Along with her specialty ice breath, she could be the one to use a few of the things that all three can do such as the laser eyes, forming tornadoes, etc, as well as stuff that fits her more technical character, like fancy flying maneuvers or a counter. Also apparently her bow has a bomb built into it in one episode, so that'd give her a gadget to use.
Bubbles: Support. She'd still have punching. flying and her specialty sonic screams, but also she could provide buffs/debuffs, status effects, and summon Bullet the Squirrel as an assist, in reference to her being able to talk to animals.
Buttercup: Bruiser. Since she has no real unique abilities besides being the best in terms of super strength, she'd be based almost exclusively around bare knuckle brawling, maybe a command grab or something so she's not too basic.