Sequential courses of anticancer target therapy lead to selection of drug-resistant cells, which results in continuous decrease of clinical response. Here we present a new approach for predicting effective combinations of target drugs, which act in a synergistic manner. Synergistic combinations of drugs may prevent or postpone acquired resistance, thus increasing treatment efficiency. We cultured human ovarian carcinoma SKOV-3 and neuroblastoma NGP-127 cancer cell lines in the presence of Tyrosine Kinase Inhibitors (Pazopanib, Sorafenib, and Sunitinib) and Rapalogues (Temsirolimus and Everolimus) for four months and obtained cell lines demonstrating increased drug resistance. We investigated gene expression profiles of intact and resistant cells by microarrays and analyzed alterations in 378 cancer-related signaling pathways using the bioinformatical platform Oncobox. This revealed numerous pathways linked with development of drug resistant phenotypes. Our approach is based on targeting proteins involved in as many as possible signaling pathways upregulated in resistant cells. We tested 13 combinations of drugs and/or selective inhibitors predicted by Oncobox and 10 random combinations. Synergy scores for Oncobox predictions were significantly higher than for randomly selected drug combinations. Thus, the proposed approach significantly outperforms random selection of drugs and can be adopted to enhance discovery of new synergistic combinations of anticancer target drugs.