In a previous paper, sufficiently large-amplitude and left-handed pump waves propagating parallel to the background magnetic field were shown to stabilize a moderately dense beam in a proton plasma against the generation of waves drawing their energy from the differential streaming motion of the beam <Gomberoff, 2003>. We now examine the general case of both left-hand and right-hand pump waves and their effects on beam instability as a function of pump wave amplitude and frequency, beam speed, and plasma component temperatures. We find that the left-hand pump wave always gives beam stability above a threshold amplitude. Larger threshold trend with increasing beam speed and lower ones with increasing temperature. It is also shown that they can stabilize left-hand polarized instabilities in the case of large drift velocities. The right-hand pump similarly suppresses beam instabilities when its pump frequency is below the linearly unstable range of frequencies. However, when its pump frequency is within the range of instability, that part of the range below the pump frequency is stabilized beyond a threshold amplitude, but the part above becomes even more unstable in the presence of a right-hand pump.