Top walls sashay to opposite side (if gendered: "Drive in the right lane, men passing back to back")
Side walls advance, left hand allemande, retire
Top walls sashay home
Everyone dosido partner, 
do-SA-do partner, 
promenade to next WALL. 
Do the dance four times with calls, four times "on your own"
Possible
 prep practice: Tops advance, meet/identify your opposite, retire. Sides
 in, identify, retire. All promenade to next wall. 
Depending
 on size of hall, number of couples, and experience level/sobriety of 
dancers, this could either be cleanly/tightly phrased or a total 
pig-pile, sorta like Foula Reel. 
I'm going to totally try this at our 
(small, square-shaped, local, fun-loving and open-minded) Peirce's Hall 
this weekend, if Steve Howland will share the mic for a moment, but before I do:
Does this already exist, and I've just forgotten?
Or anything similar? 
Does it work in real life, with the right crowd/band/hall?
Kinda excited to find out...
Cheers,
Amy