We present a new precision radial velocity (RV) data set that reveals a multi-planet system orbiting the G0V star HD 34445. Our 18-year span consists of 333 precision RV observations, 56 of which were previously published and 277 of which are new data from the Keck Observatory, Magellan at Las Campanas Observatory, and the Automated Planet Finder at Lick Observatory. These data indicate the presence of six planet candidates in Keplerian motion about the host star with periods of 1057, 215, 118, 49, 677, and 5700 days, and minimum masses of 0.63, 0.17, 0.1, 0.05, 0.12, and 0.38 MJ, respectively. The HD 34445 planetary system, with its high degree of multiplicity, its long orbital periods, and its induced stellar RV half-amplitudes in the range 2 m/s~<K~<5 m/s is fundamentally unlike either our own solar system (in which only Jupiter and Saturn induce significant reflex velocities for the Sun), or the Kepler multiple-transiting systems (which tend to have much more compact orbital configurations).