We present new, high-precision Doppler radial velocity (RV) data sets for the nearby K3V star HD 219134. The data include 175 velocities obtained with the HIRES Spectrograph at the Keck I Telescope and 101 velocities obtained with the Levy Spectrograph at the Automated Planet Finder Telescope at Lick Observatory. Our observations reveal six new planetary candidates, with orbital periods of P = 3.1, 6.8, 22.8, 46.7, 94.2, and 2247 days, spanning masses of M sin i = 3.8, 3.5, 8.9, 21.3, 10.8, and 108 M-circle plus, respectively. Our analysis indicates that the outermost signal is unlikely to be an artifact induced by stellar activity. In addition, several years of precision photometry with the T10 0.8 m automatic photometric telescope at Fairborn Observatory demonstrated a lack of brightness variability to a limit of similar to 0.0002 mag, providing strong support for planetary-reflex motion as the source of the RV variations. The HD 219134 system with its bright (V = 5.6) primary provides an excellent opportunity to obtain detailed orbital characterization (and potentially follow-up observations) of a planetary system that resembles many of the multiple-planet systems detected by Kepler, which are expected to be detected by NASA's forthcoming TESS Mission and by ESA's forthcoming PLATO Mission.