It doesn’t matter if there is 1 Capt or 4 Capts. Only one of them is the PIC for the whole flight. I doubt changing the makeup of the 4 crew is going to change the fatigue levels.
Actually it does matter.
The crew should consist of a Capt + F/O operating and a Capt + F/O augmenting and should be rostered as such. The rolls are reversed on the return sector allowing the Augmenting crew of the first sector to be the operating of the second and vis versa. So different PIC for each individual sector. Upside being planning rest for the duty both prior to the pattern and during and also promotional opportunities, downside obviously will be recency issues and CRM with 2 Capt on the flight deck.