This paper studies the supervisory control problem of nondeterministic discrete event systems with driven events in the setting of masked prioritized synchronous composition (MPSC). MPSC was extended from prioritized synchronous composition (PSC) by Kumar and Heymann [15] in order to permit systems interaction with their environment via interface masks. They also studied the supervisory control problem under the assumption that the set of driven events was empty. In this paper, the aforementioned assumption is relaxed. We first derive relations among behaviors at different levels of the system. Next, we solve the supervisor synthesis problem for controlling the plant behavior as observed at the interface level. Finally, we give a necessary and sufficient condition for the existence of the supervisor for controlling the plant behavior as observed at the plant level. We establish a link between MPSC and PSC by showing that a supervisory control problem in the setting of MPSC can be transferred to a supervisory control problem in the setting of PSC under certain conditions.