Air 2000 do monitored approaches if there is ANY cloud within 200' of MDA/DH or the viz is low. However, generally if it looks like it might end up being Cat 2 or 3 weather then a monitored approach will often be briefed and flown anyway.
FO is always handling pilot for monitored approach. Control is handed over prior to briefing, which generally means before TOD.
The FO will brief the descent/approach.
FO looks in, Captain looks out. FO makes all the calls. At decision, Captain calls either land or go-around. If its go-around, the FO maintains control and flys the missed approach. If the call is land, the Captain takes control and flys the final part.
UNLESS its a Cat 3b no decision height, in which case the Captain takes control on main gear touchdown.
If a monitored approach is started and it is obviously reasonable weather then the Captain will call visual a lot earlier, and if still at a safe height and the FO is happy, the FO can continue with a normal approach to land, Cat 1, if it was his sector anyway.
So
FO always flys the approach
FO flys the go-around
Captain takes over at the "decide" call if the call is land
If Captains sector, FO given control prior to TOD
If FOs sector, FO stays as PF
Hope that helps.
Seems to work.