  Since the discovery of a Higgs boson at the LHC and the measurement of many
of its branching ratios, there have been numerous studies exploring the
restrictions these results place on the parameter space of two Higgs doublet
models. We extend these results to include the full data set and study the
expected sensitivity that can be obtained with 300 and 3000 inverse femptobarn
of integrated luminosity. We consider searches for a heavy Standard Model Higgs
boson, with a mass ranging from 200 to 400 GeV, and show that the
non-observation of such a Higgs boson can substantially narrow the allowed
regions of parameter space in two Higgs doublet models.
