In a recent Science News, it mentioned two orbiting black holes (which later combined) were precessing; i.e. their motion did not remain in a stable plane, but rather the plane itself was changing. Which seemed odd to me.
Admittedly I need to read up on precession. And maybe in the case of black holes there were other causes (gravity waves? electro-magnetic fields?) But my first thought is: maybe the size of the objects matter. So could precession happen with point masses?