A new statistical mechanical approach for studying multilayer adsorption phenomena is presented. It is shown that a multilayer adsorbed film can be treated as a multicomponent monolayer, the equilibrium equations of which are determined from the adsorption process and the processes which form the constituents of the monolayer. The derivation of the equilibrium equations is extremely simple and allows the extension of the BET isotherm to complicated systems. In this respect, the effect of the short-range lateral interactions on the properties of the BET isotherm is examined. In addition, effects coming from multisite occupancy with or without lateral interactions and from the energetic heterogeneity of the adsorbent surface affecting only the first or the first and the second sublayer are also taken into account and discussed.