Both Railroad Ink. and Number 9 (might be called 0-9) are games which are solely component limited, meaning that if you buy 2 boxes you can play with twice the amount of players (12 and 8 respectively).
Mysterium is a co-op game for up to 7 players.
If you are into deduction and quick thinking Ricochet Robots might be for you.
If you want a chill game to have a chat while playing Concept (without the rules for points) is a fun “guess the word/phrase” game.
I think you meant “powers of two” not “square numbers” near the end there