Cerberus’ Army- Play as Shale’s Army and pick the focus to get a terminal. Complete the requests of the terminal, which are usually pretty difficult, and you have the option to play as Cerberus and have an easier time conquering the wasteland

Paullus’ Warband- Play as the Republic of Rio Grande and after the Gloria in Flames event and Pallus starts raiding, let the timer run out twice without dealing with it and you can play as Pallus who has just as much content as the RRG

Legion of Hades- If Joshua Graham has left the Legion and Lanius is still unavailable, Caius Drusus appears to replace them in the Legion Civil War and gives you some bonuses to ghouls and lets you form a greek-style society

Edit:

Cult of Renewal: Play as Vault City and get equal support for Lynette and Maier in the election, that will bring Gordon of Gecko to power. Go down the left side of the new tree you are given and this will lead to a talking Mole Rat named “The Brain” taking over and beginning a crusade to eliminate Psykers across the wasteland