It has been my 48-yr experience that piston Positive Displacement (PD) pumps are used primarily where double-action effect is needed, required, or desired. Otherwise, a plunger pump is applied. I have used plungers in excess of 350 oF with no problems. I have used plungers at -350 oF & 3,000 psig with no problems. I have also used plungers with 10,000 psig discharge - also, no problems (& in one, single pumping stage).
The problems with plungers are usually centered on the properties of the applied plunger seals. The seals are the weakest point in the mechanical design. If the seals can withstand the temperature, pressure and lack of fluid lubricity, the application operates OK.
Any fluids with solids applied in a double-acting, piston PD pump with rings is going to ultimately fail as the rings wear out. The finer the solids in the fluid, the more accelerated the ring wear will be. I would NEVER apply a fluid with solids on a piston pump with rings. A plunger pump has no rings and, therefore, can sustain more fluid contamination. In the case of fluids with solids in a plunger pump, the valves result as the weakest operating component - with the seals being the next weakest point.
In short, my experience runs directly opposite of what curtis26 says. I restrict the application of ringed, double-acting piston pumps to max. 500 psig in one stage - as long as the fluid is 100% clean liquid and at ambient temperature. Plungers take more abuse, are more dependable (no ring wear), and can take more temperature and much, much higher pressures.