In 2012, the LHC discovered a new scalar particle which fits the Standard Model Higgs boson very well. However, its nature is still unknown and there are many different Beyond-the-Standard-Model theories which can fit present experimental data and have Higgs boson couplings different from the Standard Model (SM) ones. In the effective theory where the Higgs couplings to gauge bosons are even slightly different from the SM ones, the lack of unitarity cancellations could lead to large enhancements of the boson scattering cross sections. In this case, the cross section grows faster with energy for larger multiplicities, as expected from naive phase space considerations. In particular, we have found that the triple Higgs boson production from vector-boson fusion will be largely enhanced at future 33 TeV (HE-LHC) and especially 100 TeV (VHE-LHC) colliders and can be used to explore the Higgs properties with high precision.