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Semi-autonomous (SA) control of upper-limb prostheses can improve the performance and decrease the cognitive burden of a user. In this approach, a prosthesis is equipped with additional sensors (e.g., computer vision) that provide contextual information and enable the system to accomplish some tasks automatically. Autonomous control is fused with a volitional input of a user to compute the commands that are sent to the prosthesis. Although several promising prototypes demonstrating the potential of this approach have been presented, methods to integrate the two control streams (i.e., autonomous and volitional) have not been systematically investigated. In the present study, we implemented three shared control modalities (i.e., sequential, simultaneous, and continuous) and compared their performance, as well as the cognitive and physical burdens imposed on the user. In the sequential approach, the volitional input disabled the autonomous control. In the simultaneous approach, the volitional input to a specific degree of freedom (DoF) activated autonomous control of other DoFs, whereas in the continuous approach, autonomous control was always active except for the DoFs controlled by the user. The experiment was conducted in ten able-bodied subjects, and these subjects used an SA prosthesis to perform reach-and-grasp tasks while reacting to audio cues (dual tasking). The results demonstrated that, compared to the manual baseline (volitional control only), all three SA modalities accomplished the task in a shorter time and resulted in less volitional control input. The simultaneous SA modality performed worse than the sequential and continuous SA approaches. When systematic errors were introduced in the autonomous controller to generate a mismatch between the goals of the user and controller, the performance of SA modalities substantially decreased, even below the manual baseline. The sequential SA scheme was the least impacted one in terms of errors. The present study demonstrates that a specific approach for integrating volitional and autonomous control is indeed an important factor that significantly affects the performance and physical and cognitive load, and therefore these should be considered when designing SA prostheses.