Why don't Moons have Moons?

[SciTechPress]

[Jack Ryan]

Because of the way they are formed as seperate from the original planet.

In the case of our Moon it is the remnants of Thea that slammed into early Earth.

[JW Insider]

I imagine that in the initial flotsam and jetsam of stars, planets, moons, particles, rings, etc, that it would be difficult to design a stable orbit of a large satellite (moon) around an existing moon without that orbit being too much "perturbed" by the controlling planet in combination with the controlling moon. It can happen, and probably has happened a lot, but being unstable, most of them have already been thrown out of orbit. I have wondered if a dual star can have planets for the same reason. Perhaps someone knows?

[JW Insider]

Theoretically, the Sun is "orbiting" a galaxy center of mass, the Earth is a satellite orbiting the Sun, and the Moon is a satellite orbiting the Earth. NASA has even put small satellites in orbit around the Moon for short periods of time. Perhaps Cruithne, which orbits the Sun along the similar path to the Earth was once in orbit around the Moon (unlikely). It orbits the Sun once per earthly year, same as Earth. It is effectively a second moon to the Earth. But it has quite a different orbital path around the Sun: