Defects within the multilayer mirrors of EUV photomasks have been a leading challenge for EUV lithography for quite some time. By creating non-planar surfaces, they distort both the amplitude and phase of reflected light. Amplitude errors generally create a CD error on wafer, whereas phase errors tend to cause asymmetric printing through focus. Since defect-free mask blanks are not expected to be available for initial high volume EUV manufacturing, defect mitigation, compensation, and repair strategies are essential. This paper describes a technique to repair both the amplitude and phase effects of multilayer defects. For a bump defect, the phase effect (i.e. tilted Bossung curve behavior) is corrected by removing multilayer material in the vicinity of the defect. This creates a phase effect opposite to that of the defect and the two effects cancel. The amplitude error (i.e. CD error) caused by both the defect and by the phase repair is then corrected by modifying the surrounding absorber pattern. The repairs in this paper are performed by nanomachining with an AFM repair tool. The concept is validated by a combination of simulation and experimental studies with data from the Actinic Inspection Tool (AIT) at the Lawrence Berkeley National Laboratories, the EUV Alpha Demo Tool (ADT) in Albany, New York, and an AFM repair tool. The process for a complete multilayer repair is described using an example native defect repair. Encouraging results indicate that nanomachining is capable of creating the complex nano-scale three dimensional topographies required for the repair. Repair strategies for both bump and pit defects are addressed. Multiple simulation studies are used to understand the requirements for such a repair and what type of repairs may be possible.