Multispectral printer characterization requires an effective model to map the inputs to the printer (i.e., the digital counts of the inks) into reflectance spectra and vice versa. Most of the methods for printer modeling are based on the color mixing model of Neugebauer, but this model, in its original formulation, is a rather poor predictor of the printer's output, since it fails to take into account many of the relevant phenomena that take place in the printing process. These phenomena, which include light scattering within the substrate, internal and surface reflection, and ink spreading, determine an enlargement of ink drops called dot gain, which differs on the basis of the substrate condition. This paper presents a novel strategy to model dot gain and interaction among inks in the definition of a printer model based on the Yule-Nielsen spectral Neugebauer equation. The method proposed has been designed for a four-ink ink jet printer, but its formulation is general and may be extended to the characterization of devices having more than four inks. Our method requires the definition of a relatively large number of parameters, that we estimate using genetic algorithms. The model has been tested on two different printers: An Epson StylusColor™ 740 ink jet printer and an Epson StylusPhoto™ 890 ink jet printer. Using a data set consisting of 777 samples, regularly distributed in the HSV color space, we have obtained an accuracy in terms of mean root mean squared error of 0.59% and of 1.54 ΔE^*_ab for the first printer and of 1.02% and of 2.04 ΔE^*_ab for the second printer. With respect to an approach based on a single dot gain function for each ink, our approach based on many dot gain functions reduced the average root mean square error on the test set of about 40% on average.