Genetic heterogeneity and co-occurring driver mutations contribute to poor clinical outcomes in cancer. However, the impact of multiple mutations on complex signalling networks is not easily predicted. We found that, by placing mutations into their cellular context, multi-scale agent-based mathematical models could predict how genetic events combine in haematological malignancies. Simulations of lymphoma and myeloma predicted co-occurring mutations synergised to increase tumour cell expansion beyond what would be expected from the impact of the individual mutations alone. Mutational synergy between MYC and BCL2 was consistent with the more aggressive disease course of patients with double-hit lymphoma, and mutational synergy between MCL1 and CKS1B was predictive of outcome in patients with gain 1q multiple myeloma. Incorporating patient-specific mutational profiles into personalised models of lymphoma patients with the worst clinical outcomes revealed a correlation between simulated mutational synergy and overall survival, which outperformed widely used classifications of lymphoma informed by gene expression or mutational data alone. Our results demonstrated that mutational synergy scores enabled prediction of the impact of co-occurring mutations and may improve personalised prognostic predictions.