Functional electrical stimulation (FES) offers promise as a technology to restore reaching motions to individuals with spinal cord injuries. To date, the level of reaching necessary for everyday use has not been achieved due to the complexity and limitations of the arm and muscles of an individual with a spinal cord injury. To improve the performance of FES-driven reaching controllers, we developed a trajectory optimization and model predictive control scheme that incorporates knowledge of the person-specific muscle capabilities and arm dynamics. Our controller achieved 3D reaching motions with an average accuracy of 8.5 cm and demonstrated an ability to reach targets throughout the workspace. With improvements to the model, this control scheme has the potential to unlock many daily reaching tasks for individuals with spinal cord injuries.