*Completed the Vice Kings missions, haven't finished.

Let it be noted that Saints Row is innovative in that the first two Saints Row games effectively have 3 play-at-your-pace linear story arcs, the anthology of missions for each gang feels like 3 games of their own. In addition to allowing the player to choose which to start, it is non-linear in allowing you to play between arcs, so you can finish a mission of one gang's mission arc, and start a mission for another gang.
Another series (Grand Theft Auto) has done this, but not quite in the way where there is always a different mission for a different story arc available to the player for most of the playthrough.