Background: A deep understanding of carcinogenesis at the DNA level underpins many advances in cancer prevention and treatment. Mutational signatures provide a breakthrough conceptualisation, as well as an analysis framework, that can be used to build such understanding. They capture somatic mutation patterns and at best identify their causes. Most studies in this context have focused on an inherently additive analysis, e.g. by non-negative matrix factorization, where the mutations within a cancer sample are explained by a linear combination of independent mutational signatures. However, other recent studies show that the mutational signatures exhibit non-additive interactions. Results: We carefully analysed such additive model fits from the PCAWG study cataloguing mutational signatures as well as their activities across thousands of cancers. Our analysis identified systematic and non-random structure of residuals that is left unexplained by the additive model. We used hierarchical clustering to identify cancer subsets with similar residual profiles to show that both systematic mutation count overestimation and underestimation take place. We propose an extension to the additive mutational signature model—multiplicatively acting modulatory processes—and develop a maximum-likelihood framework to identify such modulatory mutational signatures. The augmented model is expressive enough to almost fully remove the observed systematic residual patterns. Conclusion: We suggest the modulatory processes biologically relate to sample specific DNA repair propensities with cancer or tissue type specific profiles. Overall, our results identify an interesting direction where to expand signature analysis.