  We study direct searches of additional Higgs bosons in multi-top-quarks
events at the LHC Run-II, its luminosity upgraded version with 3000 fb$^{-1}$,
and the International Linear Collider (ILC) with the collision energy of 1 TeV.
Additional Higgs bosons are predicted in all kinds of extended Higgs sectors,
and their detection at collider experiments is a clear signature of the physics
beyond the standard model. We consider two Higgs doublet models with the
discrete symmetry as benchmark models. If these additional Higgs bosons are
heavy enough, the decay modes including top quarks can be dominant, and the
searches in multi-top-quarks events become an important probe of the Higgs
sector. We evaluate the discovery reach in the parameter space of the model,
and find that there are parameter regions where the searches at the LHC with
3000 fb$^{-1}$ cannot survey, but the searches at the ILC 1 TeV run can. The
combination of direct searches at the LHC and the ILC is useful to explore
extended Higgs sectors.
