We report the discovery of two super-Earth mass planets orbiting the nearby K0.5 dwarf HD 7924 which was previously known to host one small planet .
The new companions have masses of 7.9 and 6.4 M _ { \oplus } , and orbital periods of 15.3 and 24.5 days .
We perform a joint analysis of high-precision radial velocity data from Keck/HIRES and the new Automated Planet Finder Telescope ( APF ) to robustly detect three total planets in the system .
We refine the ephemeris of the previously known planet using five years of new Keck data and high-cadence observations over the last 1.3 years with the APF .
With this new ephemeris , we show that a previous transit search for the inner-most planet would have covered 70 % of the predicted ingress or egress times .
Photometric data collected over the last eight years using the Automated Photometric Telescope shows no evidence for transits of any of the planets , which would be detectable if the planets transit and their compositions are hydrogen-dominated .
We detect a long-period signal that we interpret as the stellar magnetic activity cycle since it is strongly correlated with the Ca II H & K activity index .
We also detect two additional short-period signals that we attribute to rotationally-modulated starspots and a one month alias .
The high-cadence APF data help to distinguish between the true orbital periods and aliases caused by the window function of the Keck data .
The planets orbiting HD 7924 are a local example of the compact , multi-planet systems that the Kepler Mission found in great abundance .