See, that's just it. All that's really needed is a change-up of the human story. While Predator 1 was about a group of people, Predator 2 was largly based around Danny Glover's character. I mean, here are some ideas right off:
Predator hunting in Iraq, forces soilders who are libral and soilders who are conservative to set aside their differences and work together to overcome the threat.
Three predators hunting in forest durring Summer go after group of hunters. The hunters lock themselves in an old bomb shelter that the Preds slowly find ways to get inside.
Bad Blood on the loose, Predator law enforcment show up to take him down.
Durring WWII, Nazis have a Predator held captive on a remote island. (insert country here) troops storm the island and mistakingly free the Pred. When they enter the ship to escape, the Pred comes with them.
Predator in feudal Japan, two young Samurai must stop him.
A human is mistakenly brought to the Predator homeworld.
Futuristic Predator story (Pred in space or something like that)
Anyway, you get the point. If the human story remains fresh and original, the Predator can retain the same basic role in each film, with varriations here and there.