While existing detectors would see a burst of many neutrinos from a Milky Way supernova, the supernova rate is only a few per century. As an alternative, we propose the detection of approximately 1 neutrino per supernova from galaxies within 10 Mpc, in which there were at least 9 core-collapse supernovae since 2002. With a future 1 Mton scale detector, this could be a faster method for measuring the supernova neutrino spectrum, which is essential for calibrating numerical models and predicting the redshifted diffuse spectrum from distant supernovae. It would also allow a > or approximately 10(4) times more precise trigger time than optical data alone for high-energy neutrinos and gravitational waves.