We present a method for repairing defects near the top surfaces of multilayer coatings in general and specifically on extreme-ultraviolet lithography mask blanks. Milling away the defect and a surrounding region of the multilayer by use of a focused ion beam can repair both the reflectivity and the phase of the reflected light in the vicinity of such a defect. We describe the conditions under which the repaired region will not itself be a defect and experimentally demonstrate the feasibility of this multilayer repair technique. The results described are also applicable to understanding and controlling the optical effects of ion-induced multilayer erosion.