The hyperactivation of MAPK signaling pathway motivates the clinical use of MAPK inhibitors to treat BRAF-mutant melanomas. Heterogeneity in differentiation state due to epigenetic plasticity, however, results in cell-to-cell variability in the state of MAPK dependency and diminishes the efficacy of MAPK inhibitors. To identify key regulators of such variability and potential mitigation strategies, we screened 276 epigenetic-modifying compounds, individually and in combination with MAPK inhibitors, across both genetically distinct and isogenic populations of melanoma cells. Integrated with single-cell analysis and multivariate modeling, we identified three classes of epigenetic inhibitors that target seemingly distinct epigenetic states associated with either one of the lysine-specific histone demethylases KDM1A, or KDM4B, or BET bromodomain proteins. While melanocytes remained insensitive, the anti-tumor efficacy of each inhibitor was predicted based on a melanoma cell's differentiation state and MAPK activity. Our systems pharmacology approach highlights an avenue toward identifying actionable epigenetic factors that extend the BRAF oncogene addiction paradigm on the basis of tumor cell differentiation state.