The effect of adding tetravalent counterions to polyelectrolytes of varying stiffness is investigated by a flat histogram Monte Carlo technique that is capable of giving the free energy of the system by direct simulation. The ensemble average of the polyelectrolyte size decreases with the amount of added salt for all chain stiffness. When examining the size distribution functions, flexible chains have narrow end-to-end distance distribution functions for all amounts of added salt. The distribution functions for semiflexible polyelectrolytes are always broader because such chains fluctuate between stretched and collapsed conformations. For stiff chains, the distribution functions show double maxima, which reflect the fact that individual chains prefer to be in elongated or compact toroid conformations, but not inbetween. This coexistence between compact and elongated conformations for stiff polyelectrolytes, when multivalent salt is added, is manifested in force-extension curves which exhibit a plateau regime in which the chain size changes markedly at a constant force.