At what point in the series will the RPG be set? (Since some characters tend to change somewhat as the series evolves.)

I guess I am wondering if there is a particular point in the timeline where adventures are assumed to occur, or if the game will be set up with the idea that we could play at any point in the sequence. (If the game is set so that play could occur anywhere, this might mean that several versions of the same characters could be appropriate. "Here is Harry at the end of book three"; that kind of thing.)

I can see advantages each way.