  We investigate the production of three Higgs bosons in the Two Real Singlet
extension of the Standard Model, where the scalar sector is augmented by two
additional real scalar fields which are singlets under the Standard Model gauge
group. The model contains three neutral CP-even scalars, allowing for resonant
production and asymmetric decay chains. We focus on the signature $p
p\,\rightarrow\,h_3\,\rightarrow\,h_1\,h_2\,\rightarrow\,h_1\,h_1\,h_1$, where
we identify $h_3$ as the heaviest scalar state, $h_2$ as the second heaviest
and the lightest, $h_1$, as the Standard Model-like Higgs boson discovered by
the Large Hadron Collider experiments. The dominant final state occurs when all
three Higgs bosons decay to bottom-anti-bottom quark pairs,
$h_1\,\rightarrow\,b\,\bar{b}$, leading to 6 $b$-jets. Taking into account all
current theoretical and experimental constraints, we determine the discovery
prospects for this channel in future runs of the Large Hadron Collider, as well
as in the high-luminosity phase.
