High levels of variability in cancer-related cellular signalling networks and a lack of parameter identifiability in large-scale network models hamper translation of the results of modelling studies into the process of anti-cancer drug development. Recently global sensitivity analysis (GSA) has been recognised as a useful technique, capable of addressing the uncertainty of the model parameters and generating valid predictions on parametric sensitivities. Here we propose a novel implementation of model-based GSA specially designed to explore how multi-parametric network perturbations affect signal propagation through cancer-related networks. We use area-under-the-curve for time course of changes in phosphorylation of proteins as a characteristic for sensitivity analysis and rank network parameters with regard to their impact on the level of key cancer-related outputs, separating strong inhibitory from stimulatory effects. This allows interpretation of the results in terms which can incorporate the effects of potential anti-cancer drugs on targets and the associated biological markers of cancer. To illustrate the method we applied it to an ErbB signalling network model and explored the sensitivity profile of its key model readout, phosphorylated Akt, in the absence and presence of the ErbB2 inhibitor pertuzumab. The method successfully identified the parameters associated with elevation or suppression of Akt phosphorylation in the ErbB2/3 network. From analysis and comparison of the sensitivity profiles of pAkt in the absence and presence of targeted drugs we derived predictions of drug targets, cancer-related biomarkers and generated hypotheses for combinatorial therapy. Several key predictions have been confirmed in experiments using human ovarian carcinoma cell lines. We also compared GSA-derived predictions with the results of local sensitivity analysis and discuss the applicability of both methods. We propose that the developed GSA procedure can serve as a refining tool in combinatorial anti-cancer drug discovery.