Poly ADP ribose polymerase (PARP) inhibitors are mainly used in treating BRCA-mutant cancers, and their application in novel therapies to expand their benefit is of interest in personalized medicine. A recent report showed that pharmacological targeting of PARP increases the sensitivity of cancer cells to EGFR inhibition, but the therapeutic value of this combination has not been fully determined. We propose a strategy of combining PARP inhibitors with bispecific antibodies that target both EGFR and Notch signalling, highlighting the difficulties posed by deregulation of Notch signalling and the enrichment of cancer stem cells (CSCs) during therapy. In the present study, we showed that although PARP plus EGFR targeting led to more penetrant and durable responses in the non-small cell lung cancer (NSCLC) PDX model, it influenced the enrichment of stem-like cells and their relative proportion. Stem-like cells were significantly inhibited in vitro and in vivo by EGFR/Notch-targeting bispecific antibodies. These bispecific antibodies were effective in PDX models and showed promise in cell line models of NSCLC, where they delayed the development of acquired resistance to cetuximab and talazoparib. Moreover, combining EGFR/Notch-targeting bispecific antibodies and talazoparib had a more substantial antitumour effect than the combination of talazoparib and cetuximab in a broad spectrum of epithelial tumours. EGFR/Notch bispecific antibodies decrease the subpopulation of stem-like cells, reduce the frequency of tumour-initiating cells, and downregulate mesenchymal gene expression. These findings suggest that combining EGFR and Notch signalling blockade can potentially increase the response to PARP blockade.