In the classic paradigm, immunoglobulins are monospecific molecules that have stable structures and two or more identical antigen-binding sites. However, we show here for the first time that the sIgA pool of human milk contains, depending on the donor, only 35±5% λ-sIgAs, 48±7% κ-sIgAs, and 17±4% of chimeric λ-κ-sIgAs. sIgA preparations contained no traces of canonical enzymes. However, all sIgA fractions eluted from several specific affinity sorbents under the conditions destroying even strong immune complexes demonstrated high catalytic activities in hydrolysis of ATP, DNA, and oligosaccharides, and phosphorylation of proteins, lipids, and oligosaccharides. Sequential re-chromatographies of the sIgA fractions with high affinity to one affinity sorbents on the second, third and then fourth affinity sorbents bearing other immobilized antigens led to the distribution of Abs and all catalytic activities all over the profiles of these chromatographies; in all cases some fractions eluted from affinity sorbents only under the conditions destroying strong immune complexes. In vitro, only an addition of reduced glutathione and milk plasma containing no Abs to two sIgA fractions with different affinity for DNA-cellulose led to a transition of up to 11-20% of Ab from one fraction to the other. Our data are indicative of the possibility of half-molecule exchange between different IgA and sIgA molecules. In addition, it cannot be excluded that during the penetration of IgAs through the specific milk barrier, the secretory component (S) and the join chain (J) can combine molecules of dimeric H(2)L(2) λ-IgAs and κ-IgAs against different antigens forming many different variants of H(4)L(4)SJ sIgA molecules. Therefore, some chimeric molecules of sIgA can contain from two to four HL-fragments to various antigens interacting with high affinity with different sorbents and catalyzing various chemical reactions. Our data essentially expand the ideas concerning explanation of the phenomenon of polyspecificity and cross-reactivity of Abs.