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We evaluate the discovery potential for the heavy Higgs bosons at the LHC energy upgrade with √s =27 TeV.We assume the degenerate mass spectrum and an approximate alignment limit in the Type-Ⅱ Two Higgs Doublet Model for illustration.We explore the observability of the heavy neutral Higgs bosons by examining the clean signals from H0 → W+ W-,ZZ via gluon-gluon fusion production.The associated production of a top quark and a charged Higgs boson via gb → tH± is adopted to predict the discovery potential of heavy charged Higgses.We also emphasize the potential importance of the electroweak production of Higgs boson pairs,i.e.pp → W* → H±A0 and pp → Z*/y* → H+H-.These are only governed by pure electroweak gauge couplings and can provide complementary information to the conventional signals in the determination of the nature of the Higgs sector.