Is it possible to destroy factions?
Yes, it's possible to destroy factions.
To do so you can join one of the factions (or more than one) and during they main quest line mission against other factions (which are usually related to wiping out their headquarters) will appear. Quest names are the following.
If you side up with BoS:
- Tactical Thinking - against Railroad;
- The Nuclear Options - against Institute.
If you side up with Railroad:
- Rockets' Red Glare - against BoS;
- The Nuclear Option - against Institute.
If you side up with Institute:
- End of the Life - against Railroad;
- Airship Down - against BoS.
If you side up with Minutemen:
- The Nuclear Option - against Institute;
- With Our Powers Combined - against BoS.
See details on these quests here.
And also you can go to any faction headquarters and kill everyone there without any quests.