The Warriors on ps2 is the absolute best game you could play for this.
No other beat em up like it.
Mug someone, smash their head off a wall, kick their ribs in as they're crawling away.
Handcuff a bitch and beat her with a nightstick while she tearfully tells you she'll do anything you want. Like cuffs are an obscure unlockable pickup but because its ps2 era rockstar, they gave every compatible NPC lines for being hit while cuffed.
And that's just random acts of aggression on the pedestrians.
Combat is solid with fairly basic but satisfying combos supplemented with grapple moves and plenty of stuff lying around the streets to hit people with.
You'll foster a loving relationship with bottles for instance, once you figure out its better to not throw them (gif related)
Oh and full co-op availability.
I still replay levels about as soon as I can bear to because its an irreplaceable game, the manner in which you go around those streets kicking the fuck out of people is second to none.
Last thing because I've been wanting to gush about this game for a while now, the language is a complete novelty compared to today's standards. Playing as one of the PCs in particular and hearing him call everyone pussies, faggots and wimps puts more of a smile on my face with each passing replay.
One of my favourite games ever and probably exactly what you're looking for
inb4 filenames, please contain your urge to bust my balls for grabbing the 1st shit I found.