The identification of cancer-promoting genetic alterations is challenging particularly in highly unstable and heterogeneous cancers, such as esophageal adenocarcinoma (EAC). Here we describe a machine learning algorithm to identify cancer genes in individual patients considering all types of damaging alterations simultaneously. Analysing 261 EACs from the OCCAMS Consortium, we discover helper genes that, alongside well-known drivers, promote cancer. We confirm the robustness of our approach in 107 additional EACs. Unlike recurrent alterations of known drivers, these cancer helper genes are rare or patient-specific. However, they converge towards perturbations of well-known cancer processes. Recurrence of the same process perturbations, rather than individual genes, divides EACs into six clusters differing in their molecular and clinical features. Experimentally mimicking the alterations of predicted helper genes in cancer and pre-cancer cells validates their contribution to disease progression, while reverting their alterations reveals EAC acquired dependencies that can be exploited in therapy.