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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 ${\mathcal{M}}\mathrm{sin}i=3.8,$ 3.5, 8.9, 21.3, 10.8, and $108\;{{\mathcal{M}}}_{\oplus }$, 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 ∼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.