Like classical chemotherapy regimens used to treat cancer, targeted therapies will also rely upon polypharmacology, but tools are still lacking to predict which combinations of molecular-targeted drugs may be most efficacious. In this study, we used image-based proliferation and apoptosis assays in colorectal cancer cell lines to systematically investigate the efficacy of combinations of two to six drugs which target critical oncogenic pathways. Drug pairs targeting key signaling pathways resulted in synergies across a broad spectrum of genetic backgrounds, but often yielded only cytostatic responses. Enhanced cytotoxicity was observed when additional processes including apoptosis and cell cycle were targeted as part of the combination. In some cases, where cell lines were resistant to paired and tripled drugs, increased expression of anti-apoptotic proteins was observed, requiring a fourth-order combination to induce cytotoxicity. Our results illustrate how high-order drug combinations are needed to kill drug-resistant cancer cells, and they also show how systematic drug combination screening together with a molecular understanding of drug responses may help define optimal cocktails to overcome aggressive cancers.