Is it possible for a moon in orbit around a planet to have a secondary moon orbiting the moon itself?
Yes, a moon can have a moon but only for a short time.
It is possible for a moon to capture an asteroid which then goes into orbit around it to become a moon.
The problem is that many moons, such as our moon, are tidally locked to the parent planet. They always show the same face to the parent planet. This causes a tidal bulge and the centre of mass of the moon is not at its centre.
Any body orbiting a moon will experience gravitational tidal stresses. The end effect of this is that the body will either crash into the moon, get broken up or get flung out of orbit.
We have put satellites into lunar orbit which are effectively moons of the moon. They tend to crash into the moon after a few years unless their orbit is corrected by thrusters.