Stimulated Brillouin scattering (SBS) amplification of probe signals is highly polarization dependent. Maximum and minimum gain values are associated with a pair of orthogonal states of polarization (SOP), which are related to the pump SOP. Since the maximum gain is much higher than the minimum, the SOP of the output probe is pulled towards that of the maximum amplification. Polarization pulling is restricted, however, by pump depletion. In this work, a new method is proposed, analyzed and demonstrated for enhanced SBS polarization pulling, using two orthogonal pumps. Here, one pump amplifies one polarization component of the probe wave, and at the same time the other pump attenuates the corresponding orthogonal component, resulting in a push-pull effect. In the undepleted regime and for equal total power, the same degree of pulling is achieved as in the single pump case, but at a significantly less signal gain. Thus, the dual pump technique can provide high pulling efficiency for stronger input signals, deferring the onset of depletion.