'has been fitting out' is a correct and usable phrase in written English.
It is used when you are talking about decorating, equipping, or furnishing a space, usually a building, to fit a particular purpose. For example, "The old warehouse has been fitting out to become a restaurant for the past few months."
Even the once innocuous garden hose has been fitted out with dangerous devices.
A shallow cave at the trailhead has been fitted out as a storeroom for gear and supplies.
Light and internal symmetry have been reinstated, it has been fitted out with sympathetically designed furniture and the artist Laura Ford has created a wonderful children's area.
It's been set up in the Olympic ice skating arena, which has been fitted out with briefing rooms, ISDN lines, delegation offices and hundreds of workstations.
For these children's shows, the Victor Herbert score has been fitted out with a new book and lyrics by Kevin Connors, a Fairfield resident.
The inspection report says the centre has been fitted out to a very high standard, with a kitchen and sitting room in each family apartment.
Pixar doesn't use celluloid in the creation of these works and, in many cases, they don't use celluloid to show them, since their proper home is a cinema that has been fitted out for digital projection.
Noting the presence of Confederate naval officers aboard the Laurel, he added, "There is no doubt but the expedition has been fitted out for a piratical cruise against the United States, either in this or some other vessel.
Young Africa's director, Aksana Varela, and her team are proud of their efforts: the centre has been fitted out with ramps, lecturers have been trained in sign language and assistive computer software installed in the library.
The new media centre has been fitted out with macs, printers and design software as well as reference books and a picture archive to enable prisoners to learn media production skills that will be transferable to the workplace.
