You could have storylines very much like the ones in our fan-fcs, with bigger storys than were on the Muppet Show. The Muppet Show part of the story can provide the usual skits/sketches etc, but then the house/backstage could be ongoing storys from one week to the next, with continued romances, troubles, etc.
So, Janice (for example) may break up with Floyd at the end of one episode providing a cliff hanger to the next episode where they doin't get on and there in another story line, then in the third episode they get back together...Etc
Like any regular series/soap/etc