The RN have used "5th Watch manning" for its fishery protection ships in the past. I'm not sure whether they still do, or whether it has ever been trialled on FF/DD ships but I doubt it due to the additional complexity and maintenance requirements of th FF/DD.
Like its name suggests, each ship had a Crew of 5 watches - 4 were at sea with the 5th Watch on leave or on courses etc. one Watch rotated through every X weeks. Not sure how frequently.
I suggest that this works ok in a Patrol vessel in home waters but probably not in a more complex and lean manned Warship on a long deployment, where you have to have the full range of worked up ship fighting/ operating/ maintenance skills at all times to cope with any change in circumstance and tasking.