Due to increasing printing accuracies and the possibility of printing several droplets at the same pixel location, there is a renewed interest in dot-on-dot printing models. In the present contribution, we improve a dot-on-dot spectral prediction model relying on the Yule-Nielsen modified Spectral Neugebauer model by taking into account ink spreading in all ink superposition conditions. Since ink spreading is different when ink dots are printed alone, printed in superposition with one ink or printed in superposition with two inks, we create for each superposition condition an ink spreading function mapping nominal to effective dot surface coverages. When predicting the reflection spectrum of a dot-on-dot halftone patch, its known nominal surface coverage values are converted into effective coverage values by weighting the contributions from different ink spreading functions according to the corresponding ratio of colorant surface coverages. We analyze the colorimetric prediction improvement brought by our ink spreading model for dot-on-dot thermal transfer prints and for ink-jet prints. Accounting for ink spreading according to different ink superposition conditions considerably improves the prediction accuracy. In the case of ink jet prints at 120 lpi, the mean DeltaE_94 difference between predictions and measurements is reduced from 4.54 to 1.55 (accuracy improvement factor: 3). Due to the slight misregistration between the ink layers, spectral predictions accounting for ink spreading in the case of dot-on-dot screens are less accurate than corresponding predictions for classical mutually rotated screens.