Most AvP stories usually feature a group of ordinary (relatively speaking) people who discover the creatures for the first time and get caught between them, but both the A and P series establish the presence of a powerful human organization that not only knows of the creatures' existence, but is actively trying to acquire a specimen. After the events of the Alien movies, it wouldn't be a stretch to think that there is at least one government or corporate entity that is aware of both aliens and predators and is seeking them out.
The next AvP movie could focus on the story of one or more persons who come into the employ of this organization and then, well, you know the drill. Corruption, conspiracies, secrets, plot twists, and shocking discoveries all lead to a cataclysmic showdown between the three species.