In this paper we extend the authors’ previous works by considering a multi-attribute aggregation model based on a composition of a polynomial function over a finite distributive lattice with local utility functions; these are referred to as pseudo-polynomial functions. We present an axiomatization for this class of pseudo-polynomial functions which differs from the previous ones both in flavour and nature, and develop general tools which are then used to obtain all possible such factorizations of a given pseudo-polynomial function.