Mammalian SWI/SNF (BAF) chromatin remodelers play dosage-sensitive roles in many human malignancies and neurologic disorders. The gene encoding the BAF subunit actin-like 6a (ACTL6A) is amplified early in the development of many squamous cell carcinomas (SCCs), but its oncogenic role remains unclear. Here we demonstrate that ACTL6A overexpression leads to its stoichiometric assembly into BAF complexes and drives their interaction and engagement with specific regulatory regions in the genome. In normal epithelial cells, ACTL6A was substoichiometric to other BAF subunits. However, increased ACTL6A levels by ectopic expression or in SCC cells led to near saturation of ACTL6A within BAF complexes. Increased ACTL6A occupancy enhanced polycomb opposition genome-wide to activate SCC genes and facilitated the co-dependent loading of BAF and TEAD-YAP complexes on chromatin. Both mechanisms appeared to be critical and function as a molecular AND gate for SCC initiation and maintenance, thereby explaining the specificity of the role of ACTL6A amplification in SCCs.