  Electronic localization-delocalization has played a prominent role in
realizing beyond-Landau metallic quantum critical points. It typically involves
local spins induced by strong correlations. Systems that contain local
multipolar moments offer new platforms to explore such quantum criticality.
Here, we use an analytical method at zero temperature to study the fate of an
SU(4) spin-orbital Kondo state in a multipolar Bose-Fermi Kondo model, which
provides an effective description of a multipolar Kondo lattice. We show that a
generic trajectory in the parameter space contains two quantum critical points,
which are associated with the destruction of the Kondo entanglement in the
orbital and spin channels respectively. Our asymptotically exact results reveal
a global phase diagram, provides the theoretical basis for the notion of
sequential Kondo destruction, and point to new forms of quantum criticality
that may still be realized in a variety of strongly correlated metals.
