Name of a fighting game

About 15 years ago i used to play arcade machines in Mexico, these machines had multiple games in a single machine, King of Fighters, Burnout, Crazy taxi, GTA San Andreas, sometimes Vice City, and many others, I believe those consoles were xboxes the regular ones not the 360's, this specific game that I'm trying to find out about is a fighting game that let you create your own character to a certain degree, while you modified your character it was in underwear, you could add tattoos on him, the setting were underground fights, sometimes in clubs others in parking lots, but it followed a certain storyline, at one point you get to pick a woman for you, and after winning a fight later in the game you could switch that woman for another high-class woman named Electra if you choose to do so, after that there's a fight that takes place in a cabin or warehouse where your girl is kidnapped tied to a chair in a ring of fire, and you have to beat this man to free her, as far as I remember the game had decent graphics and interactive play for its time. If anyone has any guesses that would be deeply appreciated

There's a separate thread for these.

If this was OG Xbox That sounds like Def Jam: Fight for NY or MAYBE Kakuto Chojin but I'm guessing Def Jam. Otherwise it might have been a 360 because a lot of the games you name are backwards compatible.

@tokot: Yeah it really does sound like Def Jam: Fight for New York. The girl named Electra is played by Carmen Electra, and the dude you fight in the ring of fire at the end is Snoop Dog. The whole cast is famous/semi-famous hip-hop stars of the 90's-00's. And Henry Rollins. He's the trainer that helps you level up.