Mass spectrometry is widely used to probe the proteome and its modifications in an untargeted manner, with unrivalled coverage. Applied to phosphoproteomics, it has tremendous potential to interrogate phospho-signalling and its therapeutic implications. However, this task is complicated by issues of undersampling of the phosphoproteome and challenges stemming from its high-content but low-sample-throughput nature. Hence, methods using such data to reconstruct signalling networks have been limited to restricted data sets and insights (for example, groups of kinases likely to be active in a sample). We propose a new method to handle high-content discovery phosphoproteomics data on perturbation by putting it in the context of kinase/phosphatase-substrate knowledge, from which we derive and train logic models. We show, on a data set obtained through perturbations of cancer cells with small-molecule inhibitors, that this method can study the targets and effects of kinase inhibitors, and reconcile insights obtained from multiple data sets, a common issue with these data.