Lying awake with a headache the other night gave me plenty of time to think. My brain sometimes gets really creative when I have a migraine (weirdness) and my head was all full of Community and Shakespeare so of course a mash-up was eventually going to happen.
What I figured out was that the Community group could be perfectly cast in "A Midsummer Night's Dream". The Annie/Jeff/Britta/Troy group would be perfect for the Helena/Hermia/Lysander/Demetrius quadrangle. Shirley would be a great Titania. Professor Hickey would make a great Oberon. Abed is, of course, Puck. The School Board can stand in for the Duke, and the side characters like Leonard, Garret, Neil, etc, can be the mechanicals, with the exception of Bottom who must obviously be played by Chang.
The Dean would be cast as Peaseblossom, but would keep breaking character to run after Jeff.