Spekesoftly, no I don't. It is just possible that it was a postwar addition. When I was there in '57 it was the College of Air Warfare which of course catered for senior officers.
There was considerable expansion at many other messes too. The original messes had the anteroom to the right of the main entrance and the dining room ran back at right angles on the other side of the corridor.
The expansion involved increasing the length of the anteroom to nearer the east wing. A second and much larger dining room was then built at the end of the existing dining room and, I think, new kitchens off that. At the same time a number of changes were made to the east and west wings. The variations probably depended on the ground available. Typically the east and west wings were extended to the north. On some messes additional short wings were pushed out from east and/or west wings as well. Finningley was a good example of that.
The main building additional stories may have been done as part of this new cold war expansion. Another anomalous mess was, IIRC, Upwood, which also had larger than normal accommodation wings.
While Manby was an important post-war airfield and had a number of Lincoln aircraft its runway was apparently not long enough for the Canberras used by the Spec N course which instead operated from Strubby.