Even targeted chemotherapies against solid cancers show a moderate success increasing the need to novel targeting strategies. To address this problem, we designed a systems-level approach investigating the neighbourhood of mutated or differentially expressed cancer-related proteins in four major solid cancers (colon, breast, liver and lung). Using signalling and protein–protein interaction network resources integrated with mutational and expression datasets, we analysed the properties of the direct and indirect interactors (first and second neighbours) of cancer-related proteins, not found previously related to the given cancer type. We found that first neighbours have at least as high degree, betweenness centrality and clustering coefficient as cancer-related proteins themselves, indicating a previously unknown central network position. We identified a complementary strategy for mutated and differentially expressed proteins, where the affect of differentially expressed proteins having smaller network centrality is compensated with high centrality first neighbours. These first neighbours can be considered as key, so far hidden, components in cancer rewiring, with similar importance as mutated proteins. These observations strikingly suggest targeting first neighbours as a novel strategy for disrupting cancer-specific networks. Remarkably, our survey revealed 223 marketed drugs already targeting first neighbour proteins but applied mostly outside oncology, providing a potential list for drug repurposing against solid cancers. For the very central first neighbours, whose direct targeting would cause several side effects, we suggest a cancer-mimicking strategy by targeting their interactors (second neighbours of cancer-related proteins, having a central protein affecting position, similarly to the cancer-related proteins). Hence, we propose to include first neighbours to network medicine based approaches for (but not limited to) anticancer therapies.