Some other design constraints that might be nice (some are easier than others):
-No Table: All the good games so far seem to assume that you have a large, flat surface to work on. Making a game where all the pieces are held up in the air or otherwise balanced on the players might be interesting.
-Bluffing: You have access to information that your opponent doesn't, and vice versa.
-Unequal Teams: Like a "Mad Queen" game where one side has different tools than their opponent.
-Interrupted Play: There is no set limit to someone's turn length, and you keep control of the game until you run out of options or an opponent finds an opportunity to hijack you. (Like the Interruption cards in Once Upon a Time).
-Voting: Players work independently and then rank each others' work.
-Calvinball/Nomic: Within some simple limit (like, "You can't play it the same way twice" or "You have to justify it to the GM"), everything goes.
Some of these might be redundant, but there's plenty of creative ways to "take the chains off" of a game system by removing some mutual assumptions.