In recent years there has been rising interest in the field of protein-protein conjugation, especially related to bispecific antibodies (bsAbs) and their therapeutic applications. These constructs contain two paratopes capable of binding two distinct epitopes on target molecules and are thus able to perform complex biological functions (mechanisms of action) not available to monospecific mAbs. Traditionally these bsAbs have been constructed through protein engineering, but recently chemical methods for their construction have started to (re)emerge. While these have been shown to offer increased modularity, speed, and for some methods even the inherent capacity for further functionalization (e.g., with small molecule cargo), most of these approaches lacked the ability to include a fragment crystallizable (Fc) modality. The Fc component of IgG antibodies offers effector function and increased half-life. Here we report a first-in-class disulfide rebridging and click-chemistry-based method for the generation of Fc-containing, IgG-like mono- and bispecific antibodies. These are in the FcZ-(FabX)-FabY format, i.e., two distinct Fabs and an Fc, potentially all from different antibodies, attached in a homogeneous and covalent manner. We have dubbed these molecules synthetic antibodies (SynAbs). We have constructed a T cell-engager (TCE) SynAb, FcCD20-(FabHER2)-FabCD3, and have confirmed that it exhibits the expected biological functions, including the ability to kill HER2+ target cells in a coculture assay with T cells.