We study by means of nuclear magnetic resonance the self-diffusion of protein hydration water at different hydration levels across a large temperature range that includes the deeply supercooled regime. Starting with a single hydration shell (h = 0.3), we consider different hydrations up to h = 0.65. Our experimental evidence indicates that two phenomena play a significant role in the dynamics of protein hydration water: (i) the measured fragile-to-strong dynamic crossover temperature is unaffected by the hydration level and (ii) the first hydration shell remains liquid at all hydrations, even at the lowest temperature.