Certain disclosed embodiments of the present invention concern the synthesis, derivatization, conjugation to immunoglobulins and signal amplification based on discrete, relatively short polymers having plural reactive functional groups that react with plural molecules of interest. Reactive functional groups, such as hydrazides, may be derivatized with a variety of detectable labels, particularly haptens. The remaining reactive functional groups may be conjugated directly to a specific binding molecule, such as to the oxidized carbohydrate of the Fc region of the antibody. Disclosed conjugates display large signal amplification as compared to those based on molecules derivatized with single haptens, and are useful for assay methods, particularly multiplexed assays.