A high volume high pressure common rail pump for a fuel system includes pairs of pump head assemblies in phase with each other but oriented in opposition to one another about a rotating cam shaft. Pump pistons in the pump head assemblies simultaneously undergo pumping strokes via a shared two lobe cam of the rotating cam shaft. The pump may include two pairs of pump head assemblies, and each head assembly may include two pump pistons. The cam shaft includes two cams sufficiently out of phase with one another that the cam shaft always has a positive torque even when the cam lobes are symmetrical. In addition, because the pumping is done simultaneously on opposite sides of the cam shaft, the forces on the cam shaft are balanced and its support bearings experience less wear and tear.