Two of your characters, who are the most bitter of enemies most of the time, unwittingly sit down and have a chat. Maybe they met up on Chat Roulette (is that even a thing anymore?), maybe they’re a superhero and supervillain who ran into each other out of costume. Whatever the case, at least one of them (perhaps both) doesn’t know who the other is.
What do they talk about? How do they treat each other? Do they broach the subject of their rivalry, or do they steer clear of it?
This sort of conversation isn’t uncommon in fiction (or in real life, for that matter), but it does make you look at this antagonistic relationship in a different light.