1. Literally, to play a variation on traditional chess that involves multiple boards positioned at different heights (also known as "3D chess"). No, I'm not playing three-dimensional chess with you—I can barely play regular chess!

2. By extension, to engage in a very complicated or complex game, system, or strategy involving a deep understanding of the situation that one's opponents or adversaries lack. Our CEO is always playing three-dimensional chess to stay ahead of our competition. Coaching against him is like trying to play three-dimensional chess.