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 nonresonant BSM di-Higgs production that motivate non-SM kinematic correlations and multifermion 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.