Broad absorption lines (BALs) found in a significant fraction of quasar spectra identify high-velocity outflows that might be present in all quasars and could be a major factor in feedback to galaxy evolution. Understanding the nature of these flows requires further constraints on their physical properties, including their column densities, for which well-studied BALs, such as CIV {lambda}{lambda}1548,1551, typically provide only a lower limit because of saturation effects. Low-abundance lines, such as PV {lambda}{lambda}1118,1128, indicate large column densities, implying that outflows more powerful than measurements of CIV alone would indicate. We search through a sample of 2694 BAL quasars from the Sloan Digital Sky Survey III/Baryon Oscillation Spectroscopic Survey data release 9 quasar catalogue for such absorption, and we identify 81 'definite' and 86 'probable' detections of PV broad absorption, yielding a firm lower limit of 3.0-6.2 per cent for the incidence of such absorption among BAL quasars. The PV-detected quasars tend to have stronger CIV and SiIV absorption, as well as a higher incidence of LoBAL absorption, than the overall BAL quasar population. Many of the PV-detected quasars have CIV troughs that do not reach zero intensity (at velocities where PV is detected), confirming that the outflow gas only partially covers the UV continuum source. P V appears significantly in a composite spectrum of non-PV-detected BAL quasars, indicating that P V absorption (and large column densities) is much more common than indicated by our search results. Our sample of PV detections significantly increases the number of known PV detections, providing opportunities for follow-up studies to better understand BAL outflow energetics.