Drug resistance represents a major challenge to achieving durable responses to cancer therapeutics. Resistance mechanisms to epigenetically targeted drugs remain largely unexplored. We used bromodomain and extra-terminal domain (BET) inhibition in neuroblastoma as a prototype to model resistance to chromatin modulatory therapeutics. Genome-scale, pooled lentiviral open reading frame (ORF) and CRISPR knockout rescue screens nominated the phosphatidylinositol 3-kinase (PI3K) pathway as promoting resistance to BET inhibition. Transcriptomic and chromatin profiling of resistant cells revealed that global enhancer remodeling is associated with upregulation of receptor tyrosine kinases (RTKs), activation of PI3K signaling, and vulnerability to RTK/PI3K inhibition. Large-scale combinatorial screening with BET inhibitors identified PI3K inhibitors among the most synergistic upfront combinations. These studies provide a roadmap to elucidate resistance to epigenetic-targeted therapeutics and inform efficacious combination therapies.