Attaching multiple gizmos

Solution 1:

You can attach the black body(!) of multiple gizmos to one object - in that case all the gizmos will move with the object. You can attach an object only to the axle (the metal top) of a single gizmo - in that case the object will move with the gizmo. (If you could attach it to the axles of two gizmos, it wouldn't be clear which gizmo controls the movement of the object.)

If you want an object to be influenced by multiple gizmos, you have to make a chain of gizmos, e.g. wire the axle of the first piston to the body of a second piston and then the axle of the second piston to an object. Same with rotators and other gizmos (except for the animation gizmo, which is a special case).