I’ve had a fantasy for a while to write a 4D shooter - it would have the usual WASD controls, but two keys, say ZX, would move you in the fourth dimension. The game would of course only render a 3D slice of the 4D level.
Level design would be a challenge, I think the levels would have to be built procedurally as it would just make a human brain bleed.
You would be able to walk into an empty room and then translate in the fourth dimension to encounter some creatures. Or get shot out of nowhere. You could have a button to flip the axes being rendered…