Most versions of Tetris have had multiplayer, even the original 1988 arcade had 2 player competitive. Completing lines adds penalties to the other player's field depending on the version. Make the other player fill their field before yours to win.

Used to do Tetris Battle or Friends back in the day before it became Tetris 99. Was in the top 100 competitive ranked in the world. Fun stuff.

There are multiple ways actually, most recent games allow you to send garbage lines to other players by clearing yours, and doing combos and t-spins. here's an example on puyo puyo tetris from a very good player
if you wanna try it yourself, Tetrio is really cool, free and playable in browser!