Is it possible for a moon in orbit around a planet to have a secondary moon orbiting the moon itself?

An asteroid may be captured by a moon, which would then cause the asteroid to orbit the moon and turn into a moon.

The issue is that many moons, including our own, are tidally locked to their parent planets, meaning that they always face the same direction. This results in a tidal bulge, meaning that the moon's center of mass is not at its center.

Gravitational tidal stresses will affect any body orbiting a moon; ultimately, these stresses will cause the body to smash into the moon, break apart, or be propelled out of orbit.

Since we have launched satellites into lunar orbit, which are essentially moons of the moon, they will eventually collide with the moon unless thrusters are used to correct their orbit.

The answer is that a moon can have a secondary moon orbiting it, but this is extremely uncommon and hasn't been seen in our solar system. These moons, sometimes called moonmoons or submoons, would require certain circumstances in order to form and maintain stable orbits around their parent moons.