Concomitant inhibition of multiple cancer-driving kinases is an established strategy to improve the durability of clinical responses to targeted therapies. The difficulty of discovering kinase inhibitors with an appropriate multi-target profile has, however, necessitated the application of combination therapies, which can pose significant clinical development challenges. Epigenetic reader domains of the bromodomain family have recently emerged as novel targets for cancer therapy. Here we have used BROMOscan® bromodomain ligand binding assays to identify several clinical kinase inhibitors that also inhibit bromodomains with therapeutically relevant potencies and are best classified as dual kinase/bromodomain inhibitors. Nanomolar activity on BRD4 by clinical PLK1 and JAK2/FLT3 kinase inhibitors is particularly noteworthy as these combinations of activities on independent oncogenic pathways exemplify a novel strategy for rational single agent polypharmacological targeting. Importantly, cell-based data show that these dual inhibitors suppress c-Myc expression (a hallmark of BRD4 inhibition) and induce complex polypharmacological phenotypes reflecting dual kinase/bromodomain inhibition across a panel of primary human cell assay systems that model complex tissue and disease state environments (BioMAP®). Furthermore, rich structure-activity relationships for related inhibitors and co-crystal structures identify design features that enable a general platform for the rational design of dual kinase/bromodomain inhibitors.