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We study multi-Higgs final states in vector boson fusion (VBF) processes atthe LHC and at future proton-proton colliders, focusing on the prospects formeasurements at 27 TeV and at 100 TeV. We use an effective Lagrangian whichincludes higher-dimensional operators in the mass eigenstates which arerelevant to VBF processes and relate this to specific parameterizations andmodels for new physics in the Higgs sector. We derive theoretical constraintson the parameter space from the unitarity of $2\to n$ scattering amplitudes andapply the results to $V V \to hh$ and $h h h$ processes, where $V=W,Z$. As aresult, we present constraints on differential distributions as appropriate tothe study of $V V \to hh$ and $h h h$ processes.

Multi-Higgs Production and Unitarity in Vector-Boson Fusion at Future Hadron Colliders