In aviation, there is only one boss and that's the person that signs the tech log. He/she carries the overall responsibility and ultimately calls the shots. How does that compare to two anesthesists looking after one patient?
In our practice (offshore helicopters) handing over control is the norm as we land on different decks and it's the guy with the clear approach and go-around sector who does the landing, which may be different from the position the sector is flown from.
The full handover indicates a/c status, clearance status and intentions, then :
PF"you have controls"
PNF takes over and says "I have controls"
PF takes hands and feet of and confrims "your controls"
Just so at all times, the a/c is being flown hands on.
You will have to decide at which point a handover is safe and what the important parameters are to watch. Those should be included in your handover brief.