Dude, if we're down to 'chain of command', someone's screamed "AMISTAD" and all sorts of crazy crap is going down. But a fully paid captain, two fully paid FO's. The captain is the captain and may be pilot monitoring or pilot flying, the pilot flying is always pilot flying, and the relief pilot replaces whoever is on break and their role. You only revert to 'chain of command' in really rotten scenarios. But the captains are captains, the FOs are FO's, pilot monitorings are pilot monnitorings, flying pilots are flying pilots and relief pilots do whatever the person on break was doing.
Confused yet?
Nah, actually we're all a little different. Some airlines have cruise pilots which is a whole 'nother set of sillyness.
We had some issues with four-man flying on the ER when we started doing 12-plus. So the company put it's foot down and says that the "captain of record" is the captain regardless of seniority. Otherwise, it'd be like driving with a backseat driving wife: "You're doing it wrong", "Shut up, you want to fly?" "No, but you're doing it wrong!"