  Measuring the shape of the Higgs boson potential is of paramount importance
and will be a challenging task at current as well as future colliders. While
the expectations for the measurement of the trilinear Higgs self-coupling are
rather promising, an accurate measurement of the quartic self-coupling
interaction is presently considered extremely challenging even at a future 100
TeV proton-proton collider. In this work we explore the sensitivity that a muon
collider with a center of mass energy in the multi-TeV range, and luminosities
of the order of 10^35cm^-2s^-1, as presently under discussion, might provide
thanks to a rather large three Higgs-boson production and to a limited
background. By performing a first and simple analysis, we find a clear
indication that a muon collider could provide a determination of the quartic
Higgs self-coupling that is significantly better than what is currently
considered attainable at other future colliders.
