  After the discovery of the standard-model-like Higgs boson at the LHC, the
structure of the Higgs sector remains unknown. We discuss how it can be
determined by the combination of direct and indirect searches for additional
Higgs bosons at future collider experiments. First of all, we evaluate expected
excluded regions for the mass of additional neutral Higgs bosons from direct
searches at the LHC with the 14 TeV collision energy in the two Higgs doublet
models with a softly-broken $Z_2$ symmetry. Second, precision measurements of
the Higgs boson couplings at future experiments can be used for the indirect
search of extended Higgs sectors if measured coupling constant with the gauge
boson slightly deviates from the standard model value. In particular, in the
two Higgs doublet model with the softly-broken discrete symmetry, there are
four types of Yukawa interactions, so that they can be discriminated by
measuring the pattern of deviations in Yukawa coupling constants. Furthermore,
we can fingerprint various extended Higgs sectors with future precision data by
detecting the pattern of deviations in the coupling constants of the
standard-model-like Higgs boson. We demonstrate how the pattern of deviations
can be different among various Higgs sectors which predict the electroweak rho
parameter to be unity; such as models with additional an isospin singlet, a
doublet, triplets or a septet. We conclude that as long as the gauge coupling
constant of the Higgs boson slightly differs from the standard model prediction
but is enough to be detected at the LHC and its high-luminosity run or at the
International Linear Collider, we can identify the non-minimal Higgs sector
even without direct discovery of additional Higgs bosons at the LHC.
