Polymorphic HLAs form the primary immune barrier to cell therapy. In addition, innate immune surveillance impacts cell engraftment, yet a strategy to control both, adaptive and innate immunity, is lacking. Here we employed multiplex genome editing to specifically ablate the expression of the highly polymorphic HLA-A/-B/-C and HLA class II in human pluripotent stem cells. Furthermore, to prevent innate immune rejection and further suppress adaptive immune responses, we expressed the immunomodulatory factors PD-L1, HLA-G, and the macrophage "don't-eat me" signal CD47 from the safe harbor locus. Utilizing in vitro and in vivo immunoassays, we found that T cell responses were blunted. Moreover, NK cell killing and macrophage engulfment of our engineered cells were minimal. Our results describe an approach that effectively targets adaptive as well as innate immune responses and may therefore enable cell therapy on a broader scale.