"set up headquarters" is a correct and usable phrase in written English.
You can use it when you want to indicate that you, or someone else, are establishing a base of operations. For example, "The company decided to set up headquarters in Boston."
The property tycoon Richard Tice will chair the group, which has set up headquarters in Westminster.
Homeless person has set up headquarters at bank entrance; sits, with cup in hand, sweat pouring from brow.
Until the border patrol set up headquarters next to Chinati, Judd was said to be Marfa's biggest employer.
The Iraqis invaded at dawn the next day, and Republican Guard forces set up headquarters in the Sheraton.
In 1992, after an Iraqi National Congress delegation had gone to Washington and received funding from the C.I.A., he set up headquarters in northern Iraq.
Mr. Schwarzenegger instructed his transition team to begin work immediately and to set up headquarters in the state capital as soon as this weekend.
Burton sets up headquarters in a town enchantingly named Mammoth Falls.
At the beginning of 1949, Whitaker and Baxter, the directors of the A.M.A.'s National Education Campaign, entered national politics, setting up headquarters in Chicago, with a staff of thirty-seven.
Some have been returning to Iraq, gathering arms and setting up headquarters in towns in the south, where they have been trying to recruit supporters and organize demonstrations.
But it also castigated the Free Syrian Army, and other armed adversaries of the Assad government, saying insurgents did not take sufficient care to avoid deploying forces and setting up headquarters in or near densely populated areas.
In this 1976 science fiction tale, a young Asian general conquers the world without firing a shot and sets up headquarters in a small Illinois town, where he begins his reign by publicly raping a girl and boy.
