As for Bourne, I really don't see any other show other than Bourne itself happening in that theater.
@Ringwraith already laid out a multitude of procedures that theater has, those alone already put a wrench in any other show happening in there.
And beyond that, there's other factors I think people are overlooking. Since I'm reminded of discussions not too long ago when folks thought it would be easy to just put a show in Blue Man Group. Grinchmas (and its rehearsals which happen around the time of HHN) prevent that, and then there's the other factor...zero backstage space to store any sets/props.
The theater for Bourne is not a flex-space, it's made solely for the Bourne show. Any backstage space is dedicated for whatever that show needs, be it the weapons and the big moving set pieces. There is most likely zero extra space for props that don't belong to the show, and they sure as heck can't be in the way of regular operations.
When it comes to potential venues for a second show, I would take an improv show in the Horror Make-Up theater as that's a perfect sized venue for that type of show and would be honestly feasible with just a few chairs for the cast and an extra mic or two.