Double platinum on the same system?

On the Playstation, you can achieve double platinum trophies by playing the same game on PS3 and PS4. Now to my question, is that also possible on the same system, for example if I own a game, then buy it again in a trilogy or something? Or does the system recognize that I already have this game?

No, it is counted as a separate game. As long as the developers have scripted it like this. Otherwise it would be like a package.

So should I be able to collect the trophies again?