1. A computer-implemented method for prosthesis manipulation in dental prosthesis design, comprising: presenting, via a computer-implemented interface, a virtual multi-tooth prosthesis, said virtual multi-tooth prosthesis comprising two or more three-dimensional (3D) models of individual teeth, said virtual multi-tooth prosthesis being presented relative to a 3D representation of a multi-tooth area of a patient's mouth that is to be reconstructed, said computer-implemented interface running on one or more computing devices; presenting a manipulation tool that is associated with the virtual multi-tooth prosthesis, the manipulation tool comprising a first set of manipulation handles and a second set of manipulation tools, wherein members of the first set of manipulation handles are associated with characteristics of more than one of the 3D models of the individual teeth and wherein members of the second set of manipulation handles are associated with characteristics of a single 3D model of the individual teeth of the 3D models of the individual teeth; receiving a command to manipulate a subset of the individual teeth in the virtual multi-tooth prosthesis, from an operator, via the computer-implemented interface, wherein the command includes actuating the first set of manipulation handles and the second set of manipulation handles; modifying, using one or more computing devices, based on the manipulation command and based on an occlusion of the virtual multi-tooth prosthesis relative to a corresponding antagonist area of teeth, one or more parameters for the shape of the virtual multi-tooth prosthesis, said one or more parameters being related to the subset of the individual teeth; and generating production data related to the virtual multi-tooth prosthesis based on the modified one or more parameters.