I know they did a sequel, Twisted Metal Black with an online multiplayer option on PlayStation 2 (it was the first multiplayer console game I ever played). I am not sure after that though. I think the PlayStation 3 Twisted Metal game offered online multiplayer but I am not sure. I don't think it matched Black though which let you play on the regular levels in the game in multiplayer.
Sadly, Black did not match the frenetic energy of 2 though. 2 was straight up action with very optional side quests on some levels. The levels were well designed to keep the action going. Black was more an attempt at giving you an area (on some levels) about half the size of New York City with mandatory side quests versus up to 8 players (way too big, way too monotonous chasing faster characters and not enough players per map). Still, Black was fun for a while - not as long as TM 2 though.
RE: When you see a pic of a PS1, what game do you think of?