Triple-negative breast cancer (TNBC) is an aggressive subgroup of breast cancers which is treated mainly with chemotherapy and radiotherapy. Epidermal growth factor receptor (EGFR) was considered to be frequently expressed in TNBC, and therefore was suggested as a therapeutic target. However, clinical trials of EGFR inhibitors have failed. In this study, we examine the relationship between the patient-specific TNBC network structures and possible mechanisms of resistance to anti-EGFR therapy. Using an information-theoretical analysis of 747 breast tumors from the TCGA dataset, we resolved individualized protein network structures, namely patient-specific signaling signatures (PaSSS) for each tumor. Each PaSSS was characterized by a set of 1–4 altered protein–protein subnetworks. Thirty-one percent of TNBC PaSSSs were found to harbor EGFR as a part of the network and were predicted to benefit from anti-EGFR therapy as long as it is combined with anti-estrogen receptor (ER) therapy. Using a series of single-cell experiments, followed by in vivo support, we show that drug combinations which are not tailored accurately to each PaSSS may generate evolutionary pressure in malignancies leading to an expansion of the previously undetected or untargeted subpopulations, such as ER+ populations. This corresponds to the PaSSS-based predictions suggesting to incorporate anti-ER drugs in certain anti-TNBC treatments. These findings highlight the need to tailor anti-TNBC targeted therapy to each PaSSS to prevent diverse evolutions of TNBC tumors and drug resistance development.