  The discovery of the Higgs boson has led to new possible signatures for heavy
resonance searches at the LHC. Since then, search channels including at least
one Higgs boson plus another particle have formed an important part of the
program of new physics searches. In this report, the status of these searches
by the CMS Collaboration is reviewed. Searches are discussed for resonances
decaying to two Higgs bosons, a Higgs and a vector boson, or a Higgs boson and
another new resonance, with proton-proton collision data collected at
$\sqrt{s}$ = 13 TeV in the years 2016-2018. A combination of the results of
these searches is presented together with constraints on different
beyond-the-standard model scenarios, including scenarios with extended Higgs
sectors, heavy vector bosons and extra dimensions. Studies are shown for the
first time by CMS on the validity of the narrow-width approximation in searches
for the resonant production of a pair of Higgs bosons. The potential for a
discovery at the High Luminosity LHC is also discussed.
