Opus Magnum is a really cool puzzle game, and recently I discovered a fun way to play it multiplayer, which turns it from a single-player puzzle game into a kind of Competitive/Collaborative puzzle challenge. Here's how.
The first player picks a puzzle at a level all players (I've only ever played this 2P but more players are certainly possible) are comfortable with, and picks a goal (cost, area, speed). They then make a solution to the puzzle, and then pass control to the next player. The next player makes a copy of their solution and modifies it to try and get it closer to the goal. Repeat until a player can't improve upon the solution. The player with the best version wins the round! Change the player order, pick another puzzle, and play until everyone is bored.
Playing Opus this way is surprisingly fun, and you should give it a shot if you find friends who like nerdy puzzle stuff as much as you do.