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 fb(-1) and 3000 fb(-1) 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 nonobservation of such a Higgs boson can substantially narrow the allowed regions of parameter space in two Higgs doublet models.