Over the past decade, DNA and RNA aptamers have attracted keen research interest due to their ability to specifically bind targets of therapeutic relevance. However, their application is often hampered by a short serum half-life and missing effector functions. Conjugation of aptamers to antibody Fc fragments could improve pharmacokinetics, enable immune effector mechanisms, and provide an option for the introduction of desired payloads (e.g., toxins or fluorescent dyes). We developed a modular scaffold-supported system based on human IgG1 Fc fragments, which allows for its dual functionalization with moieties of interest. In our approach, two bioorthogonal, enzyme-mediated reactions were used in combination with oxime ligation and self-assembly based on PNA-DNA base pairing. Thus, an engineered synthetic peptide nucleic acid (PNA) oligomer was coupled to the C-termini of the Fc dimer upon sequence-specific sortase A-mediated transpeptidation. Hybridization of the resulting Fc-PNA conjugate with a tailored DNA aptamer that binds cancer-related hepatocyte growth factor receptor (c-MET) led to a hybrid construct which showed strong and specific binding to c-MET and was readily internalized by c-MET-overexpressing cells. To install an additional orthogonally addressable site, aldehyde tag technology was applied followed by oxime ligation with an aminooxy-bearing fluorescent dye as model cargo. Delivery of fluorescent probe specifically to c-MET-overexpressing cells was confirmed by flow cytometry. Our approach can provide access to engineered aptamer-Fc conjugates with desired target specificity and cytotoxic payloads.