Triple-negative breast cancer (TNBC) is an aggressive breast cancer subtype with poor survival outcomes. Currently, there are no targeted therapies available for TNBCs despite remarkable progress in targeted and immune-directed therapies for other solid organ malignancies. Poly (ADP-ribose) polymerase inhibitors (PARPi) are effective anticancer drugs that produce good initial clinical responses, especially in homologous recombination DNA repair-deficient cancers. However, resistance is the rule rather than the exception, and recurrent tumors tend to have an aggressive phenotype associated with poor survival. Many efforts have been made to overcome PARPi resistance, mostly by targeting genes and effector proteins participating in homologous recombination that are overexpressed during PARPi therapy. Due to many known and unknown compensatory pathways, genes, and effector proteins, overlap and shared resistance are common. Overexpression of programmed cell death-ligand 1 (PD-L1) and cancer stem cell (CSC) sparing are novel PARPi resistance hypotheses. Although adding programmed cell death-1 (PD-1)/PD-L1 inhibitors to PARPi might improve immunogenic cell death and be crucial for durable responses, they are less likely to target the CSC population that drives recurrent tumor growth. Lysine-specific histone demethylase-1A and histone deacetylase inhibitors have shown promising activity against CSCs. Combining epigenetic drugs such as lysine-specific histone demethylase-1A inhibitors or histone deacetylase inhibitors with PARPi/anti-PD-1/PD-L1 is a novel, potentially synergistic strategy for priming tumors and overcoming resistance. Furthermore, such an approach could pave the way for the identification of new upstream epigenetic and genetic signatures.