Your only requirement is to be on a save file that has beaten the game (100% not required).
While on the main menu, relative to an Xbox controller press the following button combination:
X, X, Y, Y, X, X, X, X. And you should see this screen


This makes it easy to get around levels with different characters without having back out through slow menus. Unfortunately you cannot make characters go into other character's exclusive acts.

Video version of this guide:
https://www.youtube.com/watch?v=-VIM_qvxw9g

Edits: I'm unsure if this works on keyboard or what the equivalent keys are, I only know relative to an Xbox controller (So for Playstation switch X and Y with square and triangle, and Switch with Y and X).

It is not necessary to beat every story just the main story mode.