I've written four novels I can help you out.
Right, from Predator one there is a section on Hiroshima. Perhaps a nuclear tests person witnesses an explosive that wasn't meant to go off. Perhaps it was a predator explosion device. So he is then stopped by the secret service (links back to predator 2) so they investigate saying they know what it is we've already got someone hunting the hunter.
(Enter the injured predator who has possibly been fighting this agent)
The predator is injured and escaping this 'Agent' who is in a ghille suit. The predator's camo is broken, his bio mask is destroyed his face is bleeding etc. It would be interesting seeing roles being switched.. it's always the same Predator hunts this etc why not switch it up a little.
Or
The Predator accidentally a father who went outside with a gun to check on who it was. The Predator out of fear (he is a young blood or unblooded) attacks. The child walks out and sees the Predator. The predator begins to understand why the father went out to search then he goes and gets the child and takes her/him with it. Then 20 years later they are both hunters and they go on a hunt together... <-- (one of my personal favourite stories I have written)