There are several dances out there with a progression from mad robin with current neighbors to mad robin with new neighbors. My favorite is Mad Robin Migration II improper A1 Mad robin (clockwise) Ladies allemande left 1 1/2 A2 Partner balance and swing B1 Men allemande left 1 1/2 Neighbor swing B2 Right left thru Mad Robin (counterclockwise) But it sounds from your description " the progression is from a mad robin with your old hands four sliding along the set into a mad robin with the new four" like you mean a dance with a becket progression where you mad robin with current neighbor, slide left then mad robin with next neighbors. I haven't seen a dance like that. Jim