Polyspecific immunoconjugates and antibody composites that bind a multidrug transporter protein and an antigen associated with a tumor or infectious agent are used to overcome the multidrug resistant phenotype. These immunoconjugates and composites also can be used diagnostically to determine whether the failure of traditional chemotherapy is due to the presence of multidrug resistant tumor cells, multidrug resistant HIV-infected cells or multidrug resistant infectious agents.