With The Railroad destroyed beyond all repair, the only true obstacle presently in the way of the Institute's goals are the Brotherhood of Steel. Not only must they be defeated, they must be demoralized and broken, ensuring that they never return to the Commonwealth.
Returning to Father, the next step in the Institute's bloody conquest will be revealed, with the next target for destruction being the BoS.
It is revealed that the Institute wants to avoid any future conflict with the BoS, as well, with a cunning battle plan devised, which will require for the Sole Survivor to ensure:
The takeover of Liberty Prime, through the use of a virus uploaded by a generation 1 synth
The utter destruction of the Prydwen, through the use of Liberty Prime
The emplacement of synth forces, to take over the Boston airport, and to remove all surviving BoS forces, removing any chances for the BoS to ever return home.
Either contact Dr. Li or Evan Watson, in which they will refer the Sole Survivor to Dr. Orman, who will then explain the battle plan (listed above), before giving the Sole Survivor some teleport beacons. These beacons are thrown just as grenades or mines are thrown, and upon deployment, will teleport in various synths.
The Boston airport will then need to be cleared of BoS forces, in order to gain access to three generators spread across the airport, which must be destroyed.
After the generators have been destroyed, a generation 1 synth will be teleported in, and must be protected by the Sole Survivor as it uploads a takeover virus into Liberty Prime.
During this upload period, a number of Vertibirds will be deployed from the Prydwen, with Elder Maxson himself joining the fight in a suit of power armor.
After the virus has been uploaded, the Sole Survivor will be teleported to a nearby area that is a safe distance from the airport, in which Liberty Prime will be seen bringing the Prydwen down, destroying anyone and everything in the airport, including Liberty Prime.
This effectively kills all of the BoS leadership, and should Elder Maxson not have been dealt with personally at the airport, he will meet his demise as well.
While many weapons can be looted after the Prydwen is brought down, and a few BoS stragglers will still be hanging on to life, most of the corpses, including Elder Maxson's, will be covered in the burning wreckage of the airship, making looting next to impossible.
The fire from the wreckage will also continually hurt the Sole Survivor, regardless of where they are standing, making this a persistently dangerous area to remain in.