Zombipanda
My Boom-Boom's mostly gay
I'd say set it between Origins and City, since by City evidence of an Earthquake striking Gotham is visible (and even mentioned if I recall correctly), and during that time period Batman can be less of a loner and more open to recruiting allies which allows for the multiple characters thing.
It'd also be interesting to involve the earthquake (or other natural disaster, but I think earthquake works best) affecting the map/world/buildings around you, allowing for dynamic and edge of your seat gameplay as buildings occasionally crumble around you or even under your very feet. Will add a new dimension to grappling and gliding. And since such effects are possible in games like Battlefield 4, it's doable, though may require a whole new engine.
But since the League of Assassins has already gotten appearances in Origins and City, I'd prefer they focus on another group, like the Court of Owls (which I admittedly know nothing about).
Well, my idea is for a sort of "end-of-the-career" story that ties into the themes of the game that precedes it, with a focus on Talia and Damian and a heretic branch of the League that gave birth to Azrael. I want to expand and give more prominent parts to female characters.