We report a method for accelerated nanoscale nuclear magnetic resonance imaging by detecting several signals in parallel. Our technique relies on phase multiplexing, where the signals from different nuclear spin ensembles are encoded in the phase of an ultrasensitive magnetic detector. We demonstrate this technique by simultaneously acquiring statistically polarized spin signals from two different nuclear species (1H, 19F) and from up to six spatial locations in a nanowire test sample using a magnetic resonance force microscope. We obtain one-dimensional imaging resolution better than 5 nm, and subnanometer positional accuracy.