Bring 1 inch of water to a simmer in a large pan or Dutch oven. Place celery root, rutabaga and potatoes in a large steamer basket over the water, cover and steam over medium-low heat for 20 minutes. Add garlic and continue steaming—checking the water level and replenishing as necessary—until the vegetables are fall-apart tender, 20 minutes more.
Remove the vegetables, drain the cooking liquid and return the vegetables to the pan. Add 2 tablespoons butter and mash until chunky-smooth. Gradually stir in buttermilk, salt, pepper and nutmeg.
Just before serving, stir in the remaining 2 tablespoons butter and chives.