Cancers that overexpress tyrosine kinase receptors of HER family are treated with drugs acting on these receptors. Although HER-targeting drugs have revolutionized the treatment of HER-positive cancers, high rates of primary and treatment-emergent resistance limit their clinical utility. The present inventors have now discovered that combining HER-targeting drugs with a selective inhibitor of CDK8/19 greatly improves the efficacy of such drugs, offering an improved approach to the treatment of HER-positive cancers.