For some reason I imagine there would be a moment where the protagonist teams up with the antagonist at some point in the film to battle the Predator, which would be a nice turning point in the film. I know there are plenty of ways to express that detective narrative, or at least add the flavor, and maybe this one seems outdated or cliche, but I kinda like the idea.
Imagine cops and drug lords teaming up in an urban environment to battle a Predator. Now that would a light show!!