  We analyze here a model for an adsorbate system composed of many layers by
extending a theoretical approach used to describe pattern formation on a
monolayer of adsorbates with lateral interactions. The approach shows, in
addition to a first order phase transition in the first layer, a transition in
the second layer together with evidence of a "cascade" of transitions if more
layers are included. The transition profiles, showing a staircase structure,
corroborate this picture. The adsorption isotherm that came out of this
approach is in qualitative agreement with numerical and experimental results.
