It's being made a little easier in today's update with some lower prereqs for some of the BFF events. For the quad party, it's just a matter of building party popularity, which can be helped along by some events but is also built up just by attending, so the "main event" will inevitably fire sooner or later.
Now that the game is progressing, I am thinking about alternate paths to change the relationship with the BFF, though I don't really have any specific ideas yet.