It's theoretically possible, but not likely. The Earth-Moon-Sun system is fairly stable because the Earth and Moon are relatively far away from the Sun and eve

It's theoretically possible, but not likely. The Earth-Moon-Sun system is fairly stable because the Earth and Moon are relatively far away from the Sun and everything else. When we put a satellite in orbit around the moon, the gravity of the Earth is much greater when the satellite is on the Earth's side, and much weaker when it's on the other side of the Moon. Those forces destabilize the orbit rather quickly and corrections have to be made using fuel. If the Moon were much further away, the Moon could have a moon of its own. But the further away it gets from the Earth, the more likely it is to be influenced by other objects like other planets or the Sun.