Embodiments of the present invention include a convertible prosthesis that is capable of conversion from a humeral head replacement to a reverse reconstruction without any removal of parts integrated into the patient's bony anatomy (e.g. implant stems). A desired overall implant inclination angle may be achieved by matching various implant stems with various reverse inserts, thus permitting a resection surface to be matched with an implant stem selection while also permitting a desired overall implant inclination angle to be achieved through the selection of an appropriate insert.