Our contractor came to us fresh from putting an overroof (raised on 2 x 4 furring) on another old stone house. That house had had a standing-seam metal roof to which someone had stuck foam insulation; replacing the metal would have meant sacrificing the insulation.1988, Old-House Journal, volume 16, number 5, page 51:
overroof
verb
Etymology From over- + roof.
1
To construct a roof above (an existing roof or structure).
For a square or two he ran swiftly; then he turned into a little all-night café and in the lavatory removed the evidences of his over-roof promenade from hands and clothes. When he emerged a few moments later it was to saunter slowly on toward his apartments.1913 June–December, Edgar Rice Burroughs, “What Happened in the Rue Maule”, in The Return of Tarzan, New York, N.Y.: A[lbert] L[evi] Burt Company, […], published March 1915, →OCLC, page 40: