  Current projections suggest that the LHC will have only limited sensitivity
to di-Higgs production in the Standard Model (SM), possibly even after the
completion of its high luminosity phase. Multi-Higgs final states play a
fundamental role in many extensions of the SM as they are intrinsically
sensitive to modifications of the Higgs sector. Therefore, any new observation
in multi-Higgs final states could be linked to a range of beyond the SM (BSM)
phenomena that are not sufficiently addressed by the SM. Extensions of the
Higgs sector typically lead to new phenomenological signatures in multi-Higgs
final states that are vastly different from the SM expectation. In this work,
we provide a range of signature-driven benchmark points for resonant and
non-resonant BSM di-Higgs production that motivate non-SM kinematic
correlations and multi-fermion discovery channels. Relying on theoretically
well-motivated assumptions, special attention is devoted to the particular case
where the presence of new physics will dominantly manifest itself in
multi-Higgs final states.
