We present the new method "multiconfigurational molecular dynamics with quantum transitions" (MC-MDQT) for the simulation of processes involving multiple proton transfer reactions. MC-MDQT is a mixed quantum/classical molecular dynamics method that allows the quantum mechanical treatment of the nuclear motion of multiple hydrogen atoms and accurately describes branching processes (i.e., processes involving multiple channels or pathways). MC-MDQT is based on the surface hopping method MDQT, which has already been applied to single proton transfer reactions in solution, where the nuclear motion of only the hydrogen atom being transferred is treated quantum mechanically. The direct extension of MDQT to multiple proton transfer reactions, where many hydrogen atoms must be treated quantum mechanically, is not computationally practical. In MC-MDQT a multiconfigurational self-consistent-field method is combined with MDQT to allow the quantum mechanical treatment of multiple hydrogen atoms while still including the significant correlation. The adiabatic states are expanded in a basis set of single configurations, which are products of one-particle states calculated using effective Hamiltonians derived from the occupied adiabatic state. Thus the one-particle states and the multiconfigurational adiabatic states must be calculated self-consistently. Both the MC-MDQT and the full basis set expansion MDQT methods are applied to a model system comprised of two quantum protons moving in double well potentials and one classical harmonic solvent degree of freedom. The results show that MC-MDQT incorporates the significant correlation and accurately describes branching processes. The MC-MDQT method is also used to study model systems comprised of three quantum protons and one classical solvent degree of freedom.