Recently we started playing Mansions of Madness 2nd ed. with some simple campaign rules. The goal is just to add some sense of continuity and evolving storyline to the game. Put simply you will have a chance at some smaller advances, and the possibility of eliminating or crippling Investigators. The goal for the campaign should be to see how long you can keep up the investigations before running out of investigators. We are using both the official app and Valkyrie for this.
Check out the rules here and see if it is anything you would like to try.