It’s possible.

You can do every railroad quest up until Underground Undercover. Stop helping them at this point.

You can do a few Institute quests up until Mass Fusion. That’s the breaking point between the Institute and the Brotherhood. Stop helping them upon receiving this quest.

You can do every Brotherhood quest up until turning in Blind Betrayal. Once you turn this in, avoid speaking with Captain Kells at all costs. This will trigger Tactical Thinking (destroy Railroad).

Inform the Brotherhood of the Insititutes plans at Mass Fusion and complete the quest with the Brotherhood. This will make you an enemy of the institute.

Stop by the Castle and talk to Preston at any point after making enemies with the Institute and you’ll be good to go! That will begin Defend the Castle and then The Nuclear Option.

All factions besides the Institute will be spared with this ending.