Oncogenic FGFR4 signalling represents a potential therapeutic target in many cancer types, including triple negative breast cancer (TNBC) and hepatocellular carcinoma (HCC). However, resistance to single-agent therapy directed at FGFR4 remains a major challenge, prompting the need to identify more effective combinatorial therapeutic strategies. Here, we integrated computational network modelling and experimental validation to characterise dynamic reprogramming of the FGFR4 signalling network in TNBC following FGFR4 kinase inhibition. We found that AKT, which signals downstream of FGFR4, displayed a rapid and potent reactivation following FGFR4 targeting. Through model-based simulation and systematic prediction of the effect of co-targeting specific network nodes, we predicted, and validated experimentally, strong synergism of co-targeting FGFR4 and particular ErbB kinases or AKT, but not the upstream kinase PI3K. Further, incorporation of protein expression data from hundreds of cancer cell types enabled us to adapt our model to other diverse cellular contexts, leading to the prediction that while AKT rebound occurs frequently, it is not a general phenomenon. Instead, ERK is reactivated in a subset of cell types, including the FGFR4-driven HCC cell line Hep3B. This was subsequently corroborated, and moreover, co-targeting FGFR4 and MEK in Hep3B cells markedly enhanced inhibition of cell proliferation. Overall, these findings provide novel insights into the dynamics of drug-induced network remodelling in cancer cells, highlight the impact of protein expression heterogeneity on network response to targeted therapy and identify candidate cell type-selective combination treatments for FGFR4-driven cancer.