In the framework of the unified compositeness of leptons, quarks and Higgs bosons, supplemented with the hypothesis of the vector boson dominance of the SM gauge interactions, restrictions on the universal residual fermion–boson and boson–boson interactionsare investigated. Manifestations of the universal interactions in the W+W− and ZH boson pair production at the 2 TeV e+e− linear collider are studied. Definite signaturesof these interactions are exposed, and their relations to the nonstandard triple gaugeinteractions are considered. It is shown that the unified substructure could be tested atthe collider in these processes up to the compositeness scale [Formula: see text], which liesin the naturally preferred deca-TeV region. Importance of the optimal angular cutoffsand the polarized beams is found.