Recognition of familiar as compared to unfamiliar faces is robust and resistant to marked image distortion or degradation. Here we tested the flexibility of familiar face recognition with a morphing paradigm where the appearance of a personally familiar face was mixed with the appearance of a stranger ( Experiment 1 ) and the appearance of one's own face with the appearance of a familiar face and the appearance of a stranger ( Experiment 2 ). The aim of the two experiments was to assess how categorical boundaries for recognition of identity are affected by familiarity. We found a narrower categorical boundary for the identity of personally familiar faces when they were mixed with unfamiliar identities as compared to the control condition, in which the appearance of two unfamiliar faces was mixed. Our results suggest that familiarity warps the representational geometry of face space, amplifying perceptual distances for small changes in the appearance of familiar faces that are inconsistent with the structural features that define their identities.