[dozzie]

What you look for is not a game system, but a game master. At the beginning of every decent rule book is a sentence equivalent to this: "this book is by no means definitive; if tearing it apart and throwing it out of the window is what brings you and your team most joy, you should tear it apart".

If you enjoy playing a character and you want it to be the most important aspect of the game, you need to look for something called "storytelling" and you need to find a game master who favours this playing style.

You can easily do storytelling in (otherwise heavily formalized) D&D/d20, it only takes rest of your team to agree.