The invention is in the field of therapy of antibody deficiencies such as immune diseases and inflammatory disorders. The inventors demonstrate for the first time the convergence of intestinal IgA and serum IgG responses toward the same microbial targets, under homeostatic conditions. Private anti-microbiota IgG specificities are induced in IgA-deficient patients, but are not found in IgG pools from healthy donors, partially explaining why substitutive IgG (IVIG) cannot regulate antibody deficiency-associated gut dysbiosis and intestinal translocation. Finally, in both controls and IgA-deficient patients, systemic anti-microbiota IgG responses correlate with reduced inflammation suggesting that systemic IgG responses contribute to the gut microbiota confinement. Accordingly, the invention relates to IVIGs (Intravenous immunoglobulins) composition containing at least 1% of immunoglobulins (Ig) from SIgAd (Selective IgA deficiency) patient and their use in the treatment of antibody deficiency disorders such as immune diseases, inflammatory disorders and autoimmune disease.