Immunoassays for detection of a class of closely related antigens, e.g., PCBs, have often been too specific (responding strongly to some members of the class and missing others) and no general method for adjusting the response has been described. In this paper, the difference in the response of a model immunoassay to different Kanechlors (Japanese commercial mixtures of PCBs, analogous to Aroclors in the United States) is reduced from 20- or 50-fold (depending on which antibody is used) to 3-fold when the antibodies are mixed at the proper ratio. A mathematical model based on competitive binding of two antibodies for up to four antigens has been developed and used to describe the assay performance and to predict optimum mix ratios for the antibodies used. The model (based on separate measurement of each antibody's effective Kd for each Kanechlor) provides an excellent fit to the measured mixed antibody assay response. The model is also successful in identifying cases where mixing monoclonal antibodies will not improve the response. It is thought the method described will have applicability in a variety of cases where the analytical goal is semiquantitative screening based on the total quantity of an unknown mixture of related compounds.