  We consider dark sectors with spontaneously broken gauge symmetries, where
cascade decays of the dark sector fields naturally produce multi-Higgs boson
final states along with dark matter. Our study focuses on two and three Higgs
boson final states with missing energy using a multivariate analysis with
Boosted Decision Trees. We find that the di-Higgs boson channel is quite
promising for the $\bar b b + \gamma \gamma$ and $\bar b b + \bar \ell \ell$
decay modes. The tri-Higgs boson final state with missing energy, on the other
hand, appears to be beyond the reach of the LHC in analogous channels. This may
change when fully hadronic Higgs boson decays are considered.
