  The Higgs boson quartic self-coupling in the Standard Model appears to become
zero just below the Planck scale, with interesting implications to the
stability fo the Higgs vacuum at high energies. We review the Multiple Point
Principle that suggests the quartic self-coupling should vanish exactly at the
Planck scale. Although this vanishing is not consistent with the Standard
Model, we investigate Higgs sectors extended with additional states to test
whether one may satisfy the high scale boundary condition while maintaining the
observed Higgs mass. We also test these scenarios to ensure the stability of
the vacuum at all energies below the the Planck scale and confront them with
experimental results from the LHC and Dark Matter experiments.
