  Classification and understanding of quantum phase transitions and critical
phenomena in itinerant electron systems are outstanding questions in quantum
materials research. Recent experiments on heavy fermion systems with
higher-rank multipolar local moments provide a new platform to study such
questions. In particular, experiments on
$\text{Ce}_{3}\text{Pd}_{20}\text{(Si,Ge)}_{6}$ show novel quantum critical
behaviors via two consecutive magnetic field-driven quantum phase transitions.
At each transition, the derivative of the Hall resistivity jumps
discontinuously, which was attributed to sequential Fermi surface
reconstructions. Motivated by this discovery, we consider an effective quantum
impurity model of itinerant electrons coupled to local dipolar, quadrupolar,
and octupolar moments arising from $\text{Ce}^{3+}$ ions. Using renormalization
group analyses, we demonstrate that two-stage multipolar ordering and Fermi
surface reconstruction arise depending on which multipolar moments participate
in the Fermi surface and which other moments are decoupled via Kondo
destruction.
