The identification of somatic alterations with a cancer promoting role is challenging in highly unstable and heterogeneous cancers, such as esophageal adenocarcinoma (EAC). Here we used a machine learning approach to identify cancer genes in individual patients considering all types of damaging alterations simultaneously (mutations, copy number alterations and structural rearrangements). Analysing 261 EACs from the OCCAMS Consortium, we discovered a large number of novel cancer genes that, together with well-known drivers, help promote cancer. Validation using 107 additional EACs confirmed the robustness of the approach. Unlike known drivers whose alterations recur across patients, the large majority of the newly discovered cancer genes are rare or patient-specific. Despite this, they converge towards perturbing similar biological processes, including cell cycle progression, proteasome activity, intracellular signalling, Toll-like receptor cascade and DNA replication. Recurrence of process perturbation, rather than individual genes, divides EACs into six clusters that differ in their molecular features and suggest patient stratifications for targeted treatments. Experimental validation of selected genes by mimicking the same alterations found in patients leads to cancer-related phenotypes, thus supporting their contribution to disease progression.