The connections between their stories are very loose, making this feel more like a triptych than one coherent story.

Known as fixers, these people often make the difference between getting a coherent story and running around in a state of utter hopelessness.

To make it a joke instead of a logic puzzle, the result needs to be a coherent story that isn't strictly sensible in everyday terms.

You have added in layer upon layer in order to make it sound like a coherent story.

I've seen lots of poor comedies, but not many as weak as this in the basic business of linking scenes to form a coherent story.