IgA antibodies, which are secreted onto the mucosal surface as secretory IgA antibodies (SIgAs), play an important role in preventing influenza virus infection. A recent study reported that anti-hemagglutinin (HA) head-targeting antibodies increase anti-viral functions such as hemagglutination inhibition (HI) and virus neutralization (NT), in addition to HA binding activity (reactivity) via IgA polymerization. However, the functional properties of anti-viral IgA antibodies with mechanisms of action distinct from those of anti-HA head-targeting antibodies remain elusive. Here, we characterized the functional properties of IgG, monomeric IgA, and polymeric IgA anti-HA stalk-binding clones F11 and FI6, and B12 (a low affinity anti-HA stalk clone), as well as Fab-deficient (ΔFab) IgA antibodies. We found that IgA polymerization impacts the functional properties of anti-HA stalk antibodies. Unlike anti-HA head antibodies, the anti-viral functions of anti-HA stalk antibodies were not simply enhanced by IgA polymerization. The data suggest that two modes of binding (Fab paratope-mediated binding to the HA stalk, and IgA Fc glycan-mediated binding to the HA receptor binding site (RBS)) occur during interaction between anti-stalk HA IgA antibodies and HA. In situations where Fab paratope-mediated binding to the HA stalk exceeded IgA Fc glycan-mediated binding to HA RBS, IgA polymerization increased anti-viral functions. By contrast, when IgA Fc glycan-mediated binding to the HA RBS was dominant, anti-viral activity will fall upon IgA polymerization. In summary, the results suggest that coordination between these two independent binding modules determines whether IgA polymerization has a negative or positive effect on the anti-viral functions of anti-HA stalk IgA antibodies.