The present invention concerns CAR, CAR-T and CAR-NK constructs, preferably comprising a scFv antibody fragment against a disease-associated antigen or a hapten. More preferably, the antigen is a TAA,such as Trop-2. The constructs may be administered to a subject with a disease, such as cancer, autoimmune disease, or immune dysfunction disease, to induce an immune response against disease-associated cells. Where the constructs bind to a hapten, the subject is first treated with a hapten-conjugated antibody that binds to a disease associated antigen. Therapy may be supplemented by other treatments, such as debulking procedures (e.g., surgery, chemotherapy, radiation therapy) or coadministration of other agents. More preferably, administration of the construct is preceded by predosing withan unconjugated antibody that binds to the same disease-associated antigen. Most preferably, an antibody against CD74 or HLA-DR is administered to reduce systemic immunotoxicity induced by the constructs.