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Triple negative breast cancers (TNBC) exhibit inter- and intra-tumour heterogeneity, which is reflected in diverse drug responses and interplays with tumour evolution. Here, we use TNBC patient-derived tumour xenografts (PDTX) as a platform for co-clinical trials to test their predictive value and explore the molecular features of drug response and resistance. Patients and their matched PDTX exhibited mirrored drug responses to neoadjuvant therapy in a clinical trial. In parallel, additional clinically-relevant treatments were tested in PDTXsin vivoto identify alternative effective therapies for each PDTX model. This framework establishes the foundation for anticipatory personalised therapies for those patients with resistant or relapsed tumours. The PDTXs were further explored to model PDTX- and treatment-specific behaviours. The dynamics of drug response were characterised at single-cell resolution revealing a novel mechanism of response to olaparib. Upon olaparib treatment PDTXs showed phenotypic plasticity, including transient activation of the immediate-early response and irreversible sequential phenotypic switches: from epithelial to epithelial-mesenchymal-hybrid states, and then to mesenchymal states. This molecular mechanism was exploitedex vivoby combining olaparib and salinomycin (an inhibitor of mesenchymal-transduced cells) to reveal synergistic effects. In summary, TNBC PDTXs have the potential to help design individualised treatment strategies derived from model-specific evolutionary insights.