Objective: Paralysis resulting from spinal cord injury (SCI) can have a devastating effect on multiple arm and hand motor functions. Rotary hand movements, such as supination and pronation, are commonly impaired by upper extremity paralysis, and are essential for many activities of daily living. In this proof-of-concept study, we utilize a neural bypass system (NBS) to decode motor intention from motor cortex to control combinatorial rotary hand movements elicited through stimulation of the arm muscles, effectively bypassing the SCI of the study participant. We describe the NBS system architecture and design that enabled this functionality. Methods: The NBS consists of three main functional components: 1) implanted intracortical microelectrode array, 2) neural data processing using a computer, and, 3) a noninvasive neuromuscular electrical stimulation (NMES) system. Results: We address previous limitations of the NBS, and confirm the enhanced capability of the NBS to enable, in real-time, combinatorial hand rotary motor functions during a functionally relevant object manipulation task. Conclusion: This enhanced capability was enabled by accurate decoding of multiple movement intentions from the participant's motor cortex, interleaving NMES patterns to combine hand movements, and dynamically switching between NMES patterns to adjust for hand position changes during movement. Significance: These results have implications for enabling complex rotary hand functions in sequence with other functionally relevant movements for patients suffering from SCI, stroke, and other sensorimotor dysfunctions.