  The simplest extension of the Two Higgs Doublet Model is the addition of a
real scalar singlet, S. The effects of mixing between the singlet and the
doublets can be manifested in two ways. It can modify the couplings of the 126
GeV Higgs boson, h, and it can lead to direct detection of the heavy Higgs at
the LHC. In this paper, we show that in the type-I model, for heavy Higgs
masses in the 200-600 GeV range, the latter effect will be detected earlier
than the former for most of parameter space. Should no such Higgs be discovered
in this mass range, then the upper limit on the mixing will be sufficiently
strong such that there will be no significant effects on the couplings of the h
for most of parameter space. The reverse is true in the type-II model, the
limits from measurements of the couplings of the h will dominate over the
limits from non-observation of the heavy Higgs.
