The effects arising due to counterion adsorption in interacting planar electrical double layers is studied using modified Gouy-Chapman theory. The conditions used here model clay swelling experiments that have shown a strong dependence on the choice of counterion. The results show that the swelling pressure between charged plates depends on counterion adsorption, but they do not explain the experimental data. If the adsorption is strong enough, the swelling pressure becomes so small that it is unaffected by the plate separation. The swelling pressure is also affected by the bulk electrolyte concentration, although for a given adsorption parameter the adsorbed charge density is independent of ion concentration.