The critical coagulation concentration (CCC) for the case planar particles covered by a charge-regulated membrane layer immersed in a mixed (a:b) + (c:b) electrolyte solution is evaluated theoretically. The present study extends previous analyses in that a general charged condition in the membrane layer, which mimics biological cells, is considered, and the sizes of the charged species are taken into account. We show that for particles carrying a net negative fixed charge the classic point charge model will overestimate both CCC and the electrical repulsive force between two particles. The electrical repulsive force and the total interaction energy between two particles are large if (1) the pH is high. (2) the membrane is thin, (3) the valence of counterions is low, (4) the fraction of multivalent counterions is low, and (5) the ionic strength is low. CCC is high if (1) the pH is high, (2) the valence of counter-ions is low, and (3) the size of counterions is large; these results are consistent with experimental observations in the literature.