A simple mean field theory of multilayer adsorption is applied to the problem of crossover from a strong to an intermediate substrate regime. Two different mechanisms enforcing the transition between these regimes are considered. the first mechanism results from the gradual weakening of the substrate potential in the model with nearest neighbour interaction between adsorbed particles. As a second mechanism we consider a model with a fixed strength of surface potential but with gradually increasing strength of interaction between the third nearest neighbours in the adsorbed film. It is demonstrated that these two mechanisms lead to a different sequence of phase transitions in adsorbed films. In some cases, the results of mean field calculations are compared with Monte Carlo simulations.