Arkham Asylum, Arkham City, Gotham City

I am the first to predict that Rocksteady's third (possibly last) Batman game will be called Batman: Gotham City. Here is my guess for the storyline:

The Order of Saint Dumas take up high city council positions virtually taking over the city by controlling all of its politicians and richies except Batman. Batman then finds some troubling news about the Arkham City explosion, fearing that Azrael is actually working for the League of Assassins and goes to find Ra's al Ghuls body which is taken by Bane. Batman finds out that Bane has taken over the League of Assassins and is going to use them to destroy Gotham City using the Protocol 10. He then discovers that Hush has taken over the Order of Saint Dumas.

The game, I'm guessing, will be more RPGesque and you will be able to choose one of these endings: Batman takes over Gotham (or America), Batman takes over the Order of Saint Dumas, Batman takes over the League of Assassins, Batman helps Bane and the League of Assassins, Batman helps Hush and the Order of Saint Dumas.