Epigenetic dysregulation is a common feature of cancer and creates selective vulnerabilities arising from an increased reliance on chromatin-based mechanisms that sustain malignant transcriptional states. While many chromatin regulators are broadly required for cellular viability, others function in a context-dependent manner across distinct oncogenic settings, tissue lineages, and differentiation states. Moreover, chromatin regulators often operate within multi-subunit complexes, thus epigenetic vulnerabilities emerge from coordinated complex activities rather than single genes. Here, we integrate large-scale genetic dependency maps from human cancer cell lines with curated epigenetic complex annotations to perform a systematic, multivariate analysis of complex-level epigenetic dependencies across cancer lineages. Our analysis reveals that dependencies frequently cluster among functionally related chromatin complexes and that biologically related cancer types share similar dependency patterns, consistent with shared underlying epigenetic requirements. Focusing on melanoma, we identify multiple enriched epigenetic complex dependencies, including complexes previously associated with recurrent genetic alterations or melanocyte lineage regulation, as well as a previously unrecognized vulnerability involving the H3K4 methyltransferase complex Set1C/COMPASS. This dependency is not restricted to a specific melanoma differentiation state, but genetic perturbation of CXXC1 (a complex-specific subunit) demonstrates that sensitive melanoma cell lines require Set1C/COMPASS activity to maintain global H3K4 trimethylation (H3K4me3) and cellular proliferation. Single-cell analysis further shows that loss of H3K4me3 following CXXC1 depletion is coupled to cell-cycle blockade. Integrat