Hybridoma technology is instrumental for the development of novel antibody therapeutics and diagnostics. Recent preclinical and clinical studies highlight the importance of antibody isotype for therapeutic efficacy. However, since the sequence encoding the constant domains is fixed, tuning antibody function in hybridomas has been restricted. Here, we demonstrate a versatile CRISPR/HDR platform to rapidly engineer the constant immunoglobulin domains to obtain recombinant hybridomas, which secrete antibodies in the preferred format, species, and isotype. Using this platform, we obtained recombinant hybridomas secreting Fab′ fragments, isotype-switched chimeric antibodies, and Fc-silent mutants. These antibody products are stable, retain their antigen specificity, and display their intrinsic Fc-effector functions in vitro and in vivo. Furthermore, we can site-specifically attach cargo to these antibody products via chemoenzymatic modification. We believe that this versatile platform facilitates antibody engineering for the entire scientific community, empowering preclinical antibody research.