Targeted and inducible regulation of mammalian gene expression is a broadly important capability. We engineered drug-inducible catalytically inactive Cpf1 nuclease fused to transcriptional activation domains to tune the expression of endogenous genes in human cells. Leveraging the multiplex capability of the Cpf1 platform, we demonstrate both synergistic and combinatorial gene expression in human cells. Our work should enable the development of multiplex gene perturbation library screens for understanding complex cellular phenotypes.