  The Georgi-Machacek model extends the Standard Model Higgs sector with the
addition of isospin-triplet scalar fields in such a way as to preserve the
custodial symmetry. The presence of higher-isospin scalars contributing to
electroweak symmetry breaking offers the interesting possibility that the
couplings of the 125 GeV Higgs boson to both gluons and vector boson pairs
could be larger than those of the Standard Model Higgs boson. Constraining this
possibility using measurements of Higgs production and decay at the CERN Large
Hadron Collider is notoriously problematic if a new, non-Standard Model decay
mode of the 125 GeV Higgs boson is present. We study an implementation of this
scenario in which the Georgi-Machacek model is extended by a real singlet
scalar dark matter candidate, and require that the singlet scalar account for
all the dark matter in the universe. The combination of the observed dark
matter relic density and direct detection constraints exclude singlet scalar
masses below about 57 GeV. Higgs measurements are not yet precise enough to be
very sensitive to $h\rightarrow SS$ in the remaining allowed kinematic region,
so that constraints from Higgs measurements are so far the same as in the GM
model without a singlet scalar. We also find that, above the Higgs pole, a
substantial region of parameter space yielding the correct dark matter relic
density can escape the near-future direct detection experiments DEAP and
XENON~1T for dark matter masses as low as 120 GeV and even have a direct
detection cross section below the neutrino floor for $m_S\gtrsim 150$ GeV. This
is in contrast to the singlet scalar dark matter extension of the Standard
Model, for which these future experiments are expected to exclude dark matter
masses above the Higgs pole up to the multi-TeV range.
