In these proceedings we present the main results of [1], where we explore the phenomenological
implications of multi-Higgs boson production through longitudinal vector boson scattering within
the framework of Effective Field Theories (EFTs). We derive compact expressions for effective
tree-level amplitudes involving up to four final-state Higgs bosons. Subsequently, we compute
total cross sections for scenarios relevant to the LHC, where we observe that the general Higgs
Effective Theory (HEFT) prediction avoids the strong suppression found in the Standard Model
Effective Field Theory (SMEFT), typically expected to be several orders of magnitude smaller.