This is gonna be a bit long, so forewarning.
One way PvP could be easily implemented. It could be handled via a cocoon. 4v4. Have each team once que'd start on opposite ends of the map, the map itself would have long corridors leading to the central area of the map. The entire map would be populated with trash mobs, with a veteran mob at the center. Limit each player to 5 restrasignes and 1 reversesigne. All kills(other players, trash mobs, or the veteran mob) add to your team's score. When a match is completed, the team with the higher score "wins."
This would be, I would imagine, fairly easy for Sega to implement, as it's just reusing already existing assets in the game.
For the rewards, have the winning team get 2-3 tier III augments that would drop in exploration zones, and have the losing team get 2-3 tier II augments. This makes it where everyone gets something and no one's time was wasted. It also allows for a different path for progression,without obsoleting any current content in the game.
Doing this would allow for an easy way for Sega to keep updating the mode as the game goes on(adding new augments/bosses/maps in new cocoons as later regions unlock). The mode would also have replay value because the dynamics of the fight would change based on team comp, opponent's team comp, as well as which veteran mob happened to spawn in the center, and the rewards are tangible and useful, but not so good that you'd only play the mode as you could farm the caps normally in exploration zones as is.
Since there is no currency involved you can't "one and done" it, so it'd always be a relevant mode/activity to go do when you want augment caps but are tired of killing lvl 1 mobs in central aelio and just want to do something more challenging for a change of pace.
When the title system gets implemented into NGS, they could even have some titles for getting "X amount of player kills" or "winning X amount of matches" for the players who are into that for bragging rights(maybe even tie in a 10sg reward for getting those titles).
There's other ways it could be handled I'm sure, but this is just one way that I could see it being done where people would actually play it and it wouldn't be harmful to the game.