If the electroweak symmetry breaking is originated by a strongly coupled sector, as for instance in composite Higgs models, the Higgs boson can have non-SM couplings. In such cases, the Higgs boson and the longitudinally polarized electroweak gauge bosons (V_L's) will interact strongly and at high energies there will occur an onset of multi Higgs and V_L production signalling the breakdown of perturbation theory.
We study the sensitivity to Higgs couplings in inelastic 2 to 3 and 2 to 4 processes, where the final states include both Higgs and V_L's. We find that, due to the stronger cancellations in the corresponding amplitudes compared to the usual 2 to 2 processes, large enhancements with respect to the SM can arise even for small deviations of the couplings from their SM values. We briefly explore the possible consequences of this multiparticle production at the LHC.