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${\rm W}^\pm {\rm W}^\pm {\rm H}$ production at hadron colliders throughvector boson scattering is a so far unconsidered process, which leads to aclean signature of two same-sign charged leptons and two widely separated jets.This process is sensitive to the ${\rm HHH}$ and ${\rm WWHH}$ couplings and anydeviation of these couplings from their SM predictions serves as directevidence of new physics beyond the SM. In this paper we perform a Monte Carlostudy of this process for the $\sqrt{s}=14$ TeV LHC and a $100$ TeVpp-collider, and provide projections of the constraints on the triple-Higgs and${\rm WWHH}$ quartic couplings for these environments. In particular, weconsider the impact of pileup on the expected sensitivity in this channel. Ouranalysis demonstrates that although the sensitivity to the ${\rm HHH}$ couplingis rather low, the ${\rm WWHH}$ coupling can be constrained in this channelwithin $\sim 100\%$ and $\sim 20\%$ at 95\% confidence level around the SMprediction at the HL-LHC and a 100 TeV pp-collider, respectively.

VBS ${\rm W}^\pm {\rm W}^\pm {\rm H}$ production at the HL-LHC and a 100 TeV pp-collider