There has never been a film series that took different characters, and brought them together from their own respective movies, all while keeping an established continuity over the course of the entire series. It's an idea that was never thought possible.
Roger Rabbit doesn't count. But it was the closest thing.
Murder By Death. The worlds greatest movie detectives brought together to solve a crime; comedy, yes, but still...
Also..."League of Extraordinary Gentlemen".
Oh yeah.... "Destroy All Monsters" too. In fact, lots of Godzilla movies do just this.