  We analyse the sensitivity to beyond-the-Standard-Model effects of
hadron-collider processes involving the interaction of two electroweak and two
Higgs bosons, VVHH, with V being either a W or a Z boson. We examine current
experimental results by the CMS collaboration in the context of a dimension-8
extension of the Standard Model in an effective-field-theory formalism. We show
that constraints from vector-boson-fusion Higgs-pair production on operators
that modify the Standard Model VVHH interactions are already comparable with or
more stringent than those quoted in the analysis of vector-boson-scattering
final states. We study the modifications of such constraints when introducing
unitarity bounds, and investigate the potential of new experimental final
states, such as ZHH associated production. Finally, we show perspectives for
the high-luminosity phase of the LHC.
