Introduction Triple negative breast cancer (TNBC) is a subtype of breast cancer that accounts for up to 20% of all newly diagnosed cases. Due to its recalcitrance to available targeted agents, there is an urgent need to optimise therapy in order to improve patient prognosis. We previously demonstrated that the non-receptor tyrosine kinase PYK2 promotes tumour growth in a subtype of TNBC and in a xenograft mouse model and that PYK2 is a downstream effector of EGFR, c-Met and their crosstalk signalling. Here we use a system biology approach to identify and prioritise potent drug combinations for TNBC with the help of a mathematical model we developed from the integrated EGFR-PYK2-c-Met signalling network. Material and methods A quantitative, kinetic model of the EGFR-PYK2-c-Met signalling interaction network was developed and experimentally validated using two TNBC cell lines, MDA-MB-468 and BT-20. Signalling induction and dose response experiments for potential combinations of drug pairs targeting the central nodes of the network, including EGFR, c-Met, PYK2 and STAT3 were performed and evaluated by western blot and cell viability assays to calculate drug synergism. The mathematical model was implemented in MATLAB. For model calibration and parameter estimation MATLAB’s Global Optimisation toolbox was utilised. High-performance super-computers at Monash University were employed for parameter estimation. The Chou-Talalay’s Combination Index, (CI), Bliss Independence (BI) and Coefficient of Drug Interaction (CDI) were applied to numerically assess drug combination effects. Moreover, patient-specific models were generated through the incorporation of gene and protein expression data from individual TNBC patients using a discovery patient cohort, containing 108 patients with both patient-specific transcriptomic and proteomic data. For validation, an independent cohort was obtained from the European-Genome Phenome Archive. Results and discussions Model predictions backed up by experimental in vitro data revealed that co-targeting of EGFR and PYK2 has the most synergistic effect. Furthermore, simulations of patient-specific models led to stratification of patients into subgroups showing discrete susceptibility to specific drug combinations. Conclusion These results suggest that mechanistic systems modelling is a powerful tool for the rational design, prediction and prioritisation of potent combinatorial therapies for individual patients, hence providing a concrete step towards personalised medicine for TNBC and other tumour types.