  Strange metals appear in a wide range of correlated materials. Electronic
localization-delocalization and the expected loss of quasiparticles
characterize beyond-Landau metallic quantum critical points and the associated
strange metals. Typical settings involve local spins. Systems that contain
entwined degrees of freedom offer new platforms to realize novel forms of
quantum criticality. Here, we 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, using a renormalization-group
method. We show that at zero temperature a generic trajectory in the model's
parameter space contains two quantum critical points, which are associated with
the destruction of Kondo entanglement in the orbital and spin channels
respectively. Our asymptotically exact results reveal an overall phase diagram,
provide the theoretical basis to understand puzzling recent experiments of a
multipolar heavy fermion metal, and point to a means of designing new forms of
quantum criticality and strange metallicity in a variety of strongly correlated
systems.
