When the counting rates of neutron monitors at two different cutoff rigidities are plotted against each other, steplike changes in the rigidity dependence of the modulation are observed, leading to the well-known hysteresis effect. These steplike changes are generally related to the modulation effects of solar flare-induced shocks propagating through the heliosphere. Shock acceleration as a mechanism for the steplike changes has however not yet been considered explicitly. Therefore, in this paper it is shown that the acceleration effects of multiple shocks in the outer heliosphere may indeed explain these steps.