Membrane equilibria are investigated using the Sogami potential for plate macroions. Two methods are used to calculate the ratio s of the electrolyte concentrations in the two phases in the two-phase region of colloid stability. This ratio depends sensitively on the value of the electric potential function at the midplane between the plates, phi(d). The approximation phi(d) = 0, corresponding to the neglect of double-layer overlap, is found to lead from Sogami theory to the Donnan membrane equilibrium. An exponentially decaying electric potential function is used to estimate the effect of including the double-layer overlap. It is found that the intermacroionic interactions suppress the Donnan effect, leading to a reduced value of s that is roughly constant as a function of the surface potential, for any physically realistic surface potential greater than 40 mV. It is noted that this calculation of s may provide an explanation for the relative salinity of cells and sea water.