  We extend the coverage of resonant di-Higgs searches in the $b \bar{b} b
\bar{b}$ final state to the process $p p \to H_1 \to H_2 H_2 \to b \bar{b} b
\bar{b}$, where both $H_{1,2}$ are spin-$0$ states beyond the Standard Model.
Such a process constitutes a joint discovery mode for the new states $H_1$ and
$H_2$. We present the first sensitivity study of this channel, using public LHC
data to validate our analysis. We also provide a first estimate of the
sensitivity of the search for the HL-LHC and future facilities like the HE-LHC
and FCC-hh. We analyze the discovery potential of this search for several
non-minimal scalar sector scenarios: an extension of the SM with two extra
singlet scalar fields, the two-Higgs-doublet model and a two-Higgs doublet
model plus a singlet, which captures the scalar potential features of the
NMSSM. We find that this channel represents a novel, very powerful probe for
extended Higgs sectors, offering complementary sensitivity to existing
analyses.
