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This quest is triggered when you activate the Vault 88 Radio Beacon as a part of A Model Citizen. It requires you to turn on the workshops in three other sectors of the vault. Unlocking these workshops will expand the buildable area and connect them.
Table of contents
Turn on Vault-Tec Workshop in East Sector

The East Sector Workshop can be accessed by removing a rockslide blocking the tunnel below the East Sector sign.

You will have to find the control board before you can activate any of the Workshops. Pick-up the East Sector Control Board in the room on the right at the end of the tunnel the rockslide reveals.

Follow the waypoint indicator through the tunnels to reach the Workshop. You'll come across some Ghouls, a Legendary Mirelurk, a Mirelurk Hunter and a Mirelurk Queen guarding the East Sector Workshop.

After activating the East Sector Workshop, head back into the room you found the control board. Walk through the opening in the concrete wall and scrap the limestone to reveal a cave full of Uranium. Prepare yourself for a good amount of radscorpions and radiation.
Turn on Vault-Tec Workshop in Northeast Sector

Scrap the rockslide to the left of the North-East Sector sign to find a construction site teeming with mole rats brood mothers.

Make your way through the construction site and into the dirt tunnels. You'll come across a flight of concrete stairs. Before heading up, check the room to the left to find the North-East Sector Control Board on a shelf.

The concrete stairs will lead you to an area with some Ghouls. Come back to the wooden flight of stairs in this area after you've activated the Workshop.

Head through the hole in the wall and into a tunnel which will lead you out to an area overlooking another construction site where the North-East Sector Workshop is.

More Uranium can be found by scraping nearby limestone walls. Head back to the room with the wooden staircase. Scrap the barricade upstairs to reveal University Point Pharmacy with a red door back to the Commonwealth. Exiting the building will put you in University Point.
Turn on Vault-Tec Workshop in North Sector

The North Sector can be found in the area behind the Overseer's original desk and can be accessed by removing the rockslide to the right of the North Sector sign.

Eliminate the revealed area of more mole rats and continue walking into an old subway station with some Ghouls.

Follow the train tracks to the other end of the subway tunnel — you'll see a train that's upright — to find the North Sector Control Board on a container on the middle platform. There is a barricaded entrance opposite the control board.

Follow the waypoint indicator out of the subway station and into a tunnel that will open up into a construction site where the North Sector Workshop is.

Removing the barricade that is on the middle platform where you found the control board, will lead you to a manhole below Milton General Hospital and another back back to the Commonwealth.
Activating all three Workshops will complete Explore Vault 88.