it's not exactly pvp. More of a diverging of interests. Something that makes them going after two different ends, whether they really want to hit each other or not.
Person A) goes after an object for one reason, person B) goes for another, and those reasons conflict, etc. Actual combat between the characters is entirely up to their typists. I'm thinking more along the lines of angry banter and threats that aren't often carried through on.
And I guess if people like it, I'll make it an official suggestion.
I'll give an example:
"Finally." Seth sighed, approaching the artifact. His hand outstretched to grasp it, when his ally stormed into the room. "Seth, I need that artifact!" they shouted, reaching for it, only to have Seth grasp it and pull it to himself. "And I too need it." He said, holding it in his hands.
"Seth, give me the artifact, or I swear I will regret what I will do to you."
"I'm already gone, brother. There's nothing you can do." Seth said, and with that he was, indeed, gone, his time magic having spirited him away.
Something like that. But with more angry death glares between Reaver and someone else and lots of angry threats and staredowns.