An orthodontic assembly for moving selected teeth of a patient includes a hollow aligner shell that fits over a set of selected teeth. The aligner shell supports a series of tooth moving elements, such as magnets or metal engagement plates that are fixed in place in alignment with the selected teeth. Metal plates or magnets are affixed to the selected teeth and when the aligner shell is fitted over the teeth, the magnets in the shell exert attraction or repulsion forces on the metal plates to move the selected teeth in accordance with a treatment protocol.