Cooperative sequential adsorption is here extended to multilayer coverages. We discuss two different growth rules with cooperativity either restricted to only the first layer of coverage or applied in all layers. The unrestricted variant is considered in the case where lateral growth dominates over the nucleation of terraces. The limit of completely suppressed nucleation corresponds to a morphological transition to a flat interface from one governed by the Kardar–Parisi–Zhang equation. With the restricted growth rule we find interesting behavior resulting from a competition between lateral growth at the first layer and growth on the top of nucleated islands. There is an intermediate regime between random deposition at the submonolayer coverage and asymptotic random deposition behavior. In this regime the kinetic roughening can be studied by applying sequential adsorption rate equations for cluster lengths in the first layer, with an additional geometric argument.