The invention provides hybrid constant regions and antibodies or fusion proteins incorporating the same. The hybrid constant regions include at least CH2 and CH3 regions of an IgG or IgA constant region and Cμ3 and Cμ4 regions of a Cμ constant region. The hybrids retain properties of both component constant regions. The hybrids retain the ability of a Cμ constant region to form multivalent complexes, e.g., pentameric or hexameric structures. IgG hybrids also retain IgG properties including pH-dependent FcRn binding, which is associated with a relatively long in vivo half-life, and specific binding to protein G, which facilitates purification. Depending on the isotype and subtype, the nature of the antigen and presence of additional IgG CH1 and hinge domains, IgG hybrids may also retain properties of specific binding to protein A, and effector functions ADCC, CDC and opsonization. IgA hybrids retain the property of IgA of binding to an Fc-alpha receptor CD89.