A specific antigen-binding member (ABM) comprising a specific antigen-binding moiety and an antibody Fc region comprising a CH2 domain, which is engineered for a cysteine substitution at position 108 and/or 113, wherein numbering is according to the IMGT, and wherein the antibody Fc region does not comprise an antigen-binding CH3 domain; and an ABM conjugate (ABMC) comprising the ABM and at least one heterologous molecule covalently conjugated to one or both of the cysteines at positions 108 and 113 of the CH2 domain.