A theory for heterogeneous electron transfer of multiple electrons between a metal electrode and a multilevel redox center in a polar electrolyte is developed within the context of an extended Anderson-Newns model. Analytical expressions describing the adiabatic ground state free energy curves are derived for sequential and simultaneous transfer of electrons. The dependence of the activation and reaction free energies of the process on the key parameters of the system are analyzed. It is shown that sequential and parallel mechanisms result in distinct activation patterns. An external bias is shown to have a significant effect on both the reaction and reorganization free energies, as well as the shape of the free energy curves.