The concept of mutational signatures, with its promising translational potential, provides key insights into the mutational processes underlying cancer. Current efforts are increasingly directed toward developing comprehensive catalogues of signatures linked to various tumour types and therapeutic responses. However, the existence of multiple catalogues, generated by different groups using distinct methodologies, underscores the need for standardisation across the field, and a cohesive framework that integrates established signatures remains to be fully realised. Here, we introduce a set of Bayesian algorithms that merge predefined signature catalogues with newly identified signatures, offering a systematic approach to expanding existing collections. By leveraging a diverse array of mutational signatures, our method also groups patients based on shared mutational patterns, further enhancing the translational relevance of these catalogues. We demonstrate that this approach enables the identification of both known and novel molecular subtypes across nearly 7,000 samples spanning three major cancers: breast, colon, and lung. Building on prior research, we propose a robust strategy to deepen our understanding of mutational processes in cancer.