We have extended the van der Waals and Platteeuw theory to treat multiple occupancy of a single cage of clathrate hydrates, which has not been taken into account in the original theory but has been experimentally confirmed as a real entity. We propose a simple way to calculate the free energy of multiple cage occupancy and apply it to argon clathrate structure II in which a larger cage can be occupied by two argon atoms. The chemical potential of argon is calculated treating it as an imperfect gas, which is crucial to predict accurate pressure dependence of double occupancy expected at high pressure. It is found that double occupancy dominates over single occupancy when the guest pressure in equilibrium with the clathrate hydrate exceeds 270 MPa.