In the framework of supervised classification and prediction modeling, this paper introduces a methodology based on a general formulation of combined model integration in order to improve the fit to the data. Despite of Generalized Additive Models (GAM) our approach combines not only and not necessarily estimations derived from smoothing functions, but also those provided by either parametric or nonparametric models. Because of the multiple classifier combination we have named this general class of models as Generalized Additive MultiModels (GAM-M). The estimation procedure iterates the inner algorithm which is a variant of the backfitting algorithm - and the outer algorithm which is a standard local scoring algorithm - until convergence. The performances of GAM-M approach with respect to alternative approaches are shown in some applications using real data sets. The stability of the model estimates is evaluated by means of bootstrap and cross-validation. As a result, our methodology improves the goodness-of-fit of the model to the data providing also stable estimates.