A method for treating a tumor in a subject by administering at least three of the following treatment modalities: (i) an antibody, (ii) T cells bearing a first chimeric antigen receptor (CAR), (iii) NK cells bearing a second CAR, and (iv) NKT cells bearing a third CAR. The antibody binds specifically to stage-specific embryonic antigen 4 and each CAR contains a scFv that also binds specifically to SSEA4.