The electrophoretic mobility of a planar particle covered by a charge-regulated membrane in a mixed (a:b) + (c:b) electrolyte solution, taking the effect of the sizes of charged species into account, is analyzed theoretically. The influences of the key parameters, which include the frictional coefficient of the membrane layer, pH, membrane thickness, ionic strength, valence of counterions, fixed charge density, fraction of multivalent counterions, dissociation equilibrium constant of the functional groups, and sizes of cations and anions, are discussed. We demonstrate the importance of the ionic steric effects by showing a substantial difference between the classic point-charge model and the present model.