Humoral and cellular immune responses against tumor cells and infectious agents are induced in a mammal using an antibody that binds with an epitope of an antigen that is associated with a tumor or an infectious agent, and that contains at least one &agr;-galactosyl epitope. Such an antibody is capable of forming a complex with cells that express the target epitope and with antibodies that bind &agr;-galactosyl epitopes. Suitable antibodies include molecules that contain at least one engineered glycosylation site in the constant region of the heavy chain.