We went to it in many areas of patrol years ago and since we were on four-tens, we had one overlap day. Day shift had Monday as an overlap day. Evenings had Friday and Nights had Saturday as overlap days.
The senior folks then bid for whatever shift and squad they wanted. It continued on until the more junior person got to pick or assigned what was left over.
It worked out well for us and the junior people knew that eventually they would get their turn. It also facilitated days off for people who wanted to take a fourth day off.