  We investigate a model with two real scalar fields that minimally generates
exponentially different scales in an analog of the Coleman-Weinberg mechanism.
The classical scale invariance -- the absence of dimensionful parameters in the
tree-level action, required in such a scale generation -- can naturally be
understood as a special case of the multipoint criticality principle. This
two-scalar model can couple to the Standard Model Higgs field to realize a
maximum multiplicity of criticality for field values around the electroweak
scale, providing a generalization of the classical scale invariance to a wider
class of criticality. As a bonus, one of the two scalars can be identified as
Higgs-portal dark matter. We find that this model can be consistent with the
constraints from dark matter relic abundance, its direct detection experiments,
and the latest LHC data, while keeping the perturbativity up to the Planck
scale. We then present successful benchmark points satisfying all these
constraints: The mass of dark matter is a few TeV, and its scattering cross
section with nuclei is of the order of $10^{-9}$ pb, reachable in near future
experiments. The mass of extra Higgs boson $H$ is smaller than or of the order
of 100 GeV, and the cross section of $e^+e^- \to ZH$ can be of fb level for
collision energy 250 GeV, targetted at future lepton colliders.
