The entropic repulsion between strongly overlapping electrical double-layers from two parallel amphoteric plates is described via the Donnan equilibrium in the limit of zero electric field. The plates feature charge-regulation and the inter-plate solution is in equilibrium with a reservoir of a monovalent electrolyte solution. A finite electric potential and disjoining pressure is found at contact between the plates, due to a complete discharging of the plates. For low potentials, the decay of potential and pressure is fully governed by a characteristic length scale and the contact potential. Additionally, for large separations we find a universal inverse square decay of disjoining pressure, irrespective of the contact potential. The results of the Donnan theory show quantitative agreement with self-consistent field computations that solve the full Poisson equation.