How I though it might work is that there is one common shot of the curtain opening in front of a stage after showing the name of the next performer or performers, with the act on the stage. Then each contributor makes a scene with whatever act they want on the stage. Each act ends with the curtain closing, probably with applause
, and the title of the next act comes on, on is on a placard, etc.
So to do this we first need the common stage, curtain, lighting and such. At least the layout. Then everyone can start thinking about their act.
Note: the stage setting can be completely different. In fact it doesn't even need to be a proper stage. When the curtain opens we can show anything, outer space, the beach, interiors of buildings. You get the idea.
How does that sound?