Although many asteroids are visible with amateur equipment, and at least one can be seen with the unaided eye, the size of the companion moons make them too small for amateur observers to spot.
The first asteroid moon was not discovered until 1993, and this was by the spacecraft Galileo that flew past the asteroid belt. It was not until images taken in 2004 that the asteroid Sylvia was discovered to have two moons, followed by Eugenia and its two moons. This discovery required the use of the telescope at the European Southern Observatory in Chile.
An asteroid with three or more moons has yet to be discovered.