One of my favorite aspects of PvP in some games is the presence of PvE content that players compete to complete first. The big example I can think of is Alterac Valley in ******** in certain balancing iterations it's gone through.
I think you can also see strong non-combat PvP in Lego Indiana Jones and the classic Battletoads.
Here's the basic idea:
- You challenge another player to a mission.
- Player accepts.
- You wind up in a mission map together, with separate mission goals. Ie. you're not on the same team.
- You get access to knockbacks but cannot damage eachother directly (to avoid issues with spawncamping, kinda like Lego Indiana Jones here.) You CAN knock eachother into environmental hazards.
- There might be places where damaging the other player is possible, such as at the end. The big thing is, it's disabled for most of it because rather than being a battleground, it takes on more of a race/scavenger hunt format where both players are constantly moving around a fairly linear track.
- These missions can be FvF, KvK, or FvK.
- First player to complete the mission wins, winner take most where the rewards are concerned.
The trick is, you'd need missions designed around the dynamic. Upside is, it could use existing PvE maps. But, frankly, I'd be more interested in this as a story based form of PvE along a track than the standard FPS-style battlegrounds that exist in most MMOs.
The overall design is kinda like those episodes where you have two or more characters racing for a prize. If you're of my generation, think of it as Scrooge vs. Glomgold for the treasure. It's not, "Haha! I shot you in the face!" Killing the other person is secondary at best. It's, "Get your hands off the prize. It's mine!"
Heck, maybe one approach would be that the first half is a race. One person recovers the treasure. And the second half is combat enabled, with them trying to get back to the beam out location with it. And taking a certain amount of damage causes you to drop it, letting the other person pick it up.