Game with the central mechanic being beatboxing different songs. Freestyle would be multiplayer only.

Tycoon game where you run an Opera house.

Somalian Pirates In SPAAAAAAACE!

How about a game where you play a health inspector? It could play out LA Noir style, with the overarching plot being determining the source of a massive outbreak of salmonella. Side missions would be things like going undercover at restaurants to get an idea of how sanitary they are, or filing the paperwork to shut down a bar that's been serving burgers made from spoiled meat.

The main collectibles would be take-out menus and secret recipes.

-Open world game where you play as a worker ant in a massive, country-sized (from your perspective, that is) ant hive. The goal of the game is to overthrow the oppressive ant ruling class and establish a utopia where the worker ants control the means of production. There would be somewhere around a hundred different paths to success, most of which won't be immediately obvious.

-Space smuggler game. Make as much money as you can in any way you can, don't get caught, don't get killed, and retire to a planet all your own. Think Taipan!, but in space.

-RPG where you plays as a homeless man.