A series of appliances including a first shell and a second shell can be designed to incrementally implement a treatment plan. The first and second shells can have cavities designed to receive teeth of a jaw. The first shell can be designed to interface with a first surface of a plurality of surfaces of an attachment structure to provide a first engagement force specific to a first stage of the treatment plan. The second shell can be designed to interface with a second surface of the plurality of surfaces of the attachment structure attached to the at least one tooth of the first jaw to provide a second engagement force specific to a second stage of the treatment plan.