There may be more elegant or effective solutions, but the first thing that comes to mind would be to look at arm/disarm cues. The idea would be that whenever one cue is triggered, it also triggers a disarm cue for all other cues. While those cues are disarmed, any midi trigger can be pushed and those cues won't respond. When the currently playing cue is done (or after xx number of seconds, depending on how you program it), an arm cue is triggered, putting all of the previously disarmed cues back into an armed state.
Depending on how many cues you have, or other specifics of your programming, this might get a little complicated. And again, there may be other solutions. But you can definitely achieve what you describe with this method.
Good luck!
Mark