Inferences of subsurface flow velocities using local domain ring-diagram helioseismology depend on measuring the frequency shifts of oscillation modes seen in acoustic power spectra. Current methods for making these measurements use maximum-likelihood fitting techniques to match a model of modal power to the spectra. The model typically describes a single oscillation mode, and each mode in a given power spectrum is fit independently. We present a new method that produces measurements with higher reliability and accuracy by fitting multiple modes simultaneously. We demonstrate that this method permits measuring sub-surface flows deeper into the Sun while providing higher uniformity in data coverage and velocity response closer to the limb of the solar disk. While the previous fitting method performs better for some measurements of low phase-speed modes, we find this new method to be particularly useful for high phase-speed modes and small spatial areas.