One approach to improving the results of antibody treatment of posttransplant and other lymphomas is to alter the geometry of the antibody molecule so as to enhance its cytotoxicity. When antibody alights on a cell, cytotoxicity can be exerted by initiation of apoptotic signals at the cell surface, and by recruitment of effectors to specific sites on the antibody Fc region. Other routes to cytotoxicity have been described but their generality is debatable. The effectors consist of complement, and a series of potentially cytotoxic cells (macrophages, NK cells, neutrophils and others) bearing Fc-receptors (FcR). Recent evidence suggests that the FcR-bearing cells are the more important in dealing with antibody-coated autologous cells, including tumor cells. If the antibody happens to be of the host IgG class then its Fc region (Fcgamma) will contain a site for attachment of a non-cytotoxic FcR known as FcRB (the Brambell receptor): it is this receptor, present on endothelial cells, which recycles the molecule intact if it happens to be endocytosed and thus prolongs its metabolic life. Replacement of the mouse Fcgamma by human Fcgamma is expected to have three beneficial effects: better recruitment of human effector cells, better persistence of the antibody in extracellular fluid, and removal of a major source of immunogenic epitopes. Chemical manipulations of Fab'gamma and Fcgamma modules, linking them in different geometries via their hinge regions, offers constructs with further enhancements of cytotoxicity. These include Fab2Fc2, in which the presence of dual Fc regions enhances recruitment of both complement and cellular effectors; and bispecific antibody of the same modular formula in which one of the Fab arms is specific for tumor while the other is specific for, and recruits powerfully, a cellular effector.