  We introduce and explore new heavy Higgs scenarios in the Minimal
Supersymmetric Standard Model (MSSM) with explicit CP violation, which have
important phenomenological implications that may be testable at the LHC. For
soft supersymmetry-breaking scales M_S above a few TeV and a charged Higgs
boson mass M_H+ above a few hundred GeV, new physics effects including those
from explicit CP violation decouple from the light Higgs boson sector. However,
such effects can significantly alter the phenomenology of the heavy Higgs
bosons while still being consistent with constraints from low-energy
observables, for instance electric dipole moments. To consider scenarios with a
charged Higgs boson much heavier than the Standard Model (SM) particles but
much lighter than the supersymmetric particles, we revisit previous
calculations of the MSSM Higgs sector. We compute the Higgs boson masses in the
presence of CP violating phases, implementing improved matching and
renormalization group (RG) effects, as well as two-loop RG effects from the
effective two-Higgs Doublet Model (2HDM) scale M_H+ to the scale M_S. We
illustrate the possibility of non-decoupling CP-violating effects in the heavy
Higgs sector using new benchmark scenarios named CPX4LHC.
