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We investigate the potential of precision Higgs boson coupling measurements to discover heavy Higgs bosons by performing scans of the parameter space in two-Higgs-doublet models. Our study encompasses conventional type I and type II models, as well as models in which Higgs couplings differ between the third-generation and lighter fermion generations. The scans reveal that precision measurements at the sensitivity levels projected for Higgs factories, such as the Linear Collider Facility (LCF) and the Future Circular Collider (FCC-ee) at CERN and the Circular Electron-Positron Collider (CEPC) in China, are capable of probing heavy Higgs boson masses in the multi-TeV range, with sensitivity extending beyond 5 TeV in certain scenarios. In particular, the precise determination of the charm quark Yukawa coupling at Higgs factories provides a powerful test of the hypothesis that the fermion mass hierarchy arises from an extended Higgs sector with different Higgs fields coupling to the different generations of fermions.