  If the electroweak symmetry breaking is originated from a strongly coupled
sector, as for instance in composite Higgs models, the Higgs boson couplings
can deviate from their Standard Model values. In such cases, at sufficiently
high energies there could occur an onset of multiple Higgs boson and
longitudinally polarised electroweak gauge boson (V_L) production. We study the
sensitivity to anomalous Higgs couplings in inelastic processes with 3 and 4
particles (either Higgs bosons or V_L's) in the final state. We show that, due
to the more severe cancellations in the corresponding amplitudes as compared to
the usual 2 to 2 processes, large enhancements with respect to the Standard
Model can arise even for small modifications of the Higgs couplings. In
particular, we find that triple Higgs production provides the best
multiparticle channel to look for these deviations. We briefly explore the
consequences of multiparticle production at the LHC.
