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Among heavy fermion materials, there is a set of rare-earth intermetallicswith non-Kramers Pr$^{3+}$ $4f^2$ moments which exhibit a rich phase diagramwith intertwined quadrupolar orders, superconductivity, and non-Fermi liquidbehavior. However, more subtle broken symmetries such as multipolar orders inthese Kondo materials remain poorly studied. Here, we argue that multi-spininteractions between local moments beyond the conventional two-spin exchangemust play an important role in Kondo materials near the ordered to heavy Fermiliquid transition. We show that this drives a plethora of phases withcoexisting multipolar orders and multiple thermal phase transitions, providinga natural framework for interpreting experiments on the Pr(TM)$_2$Al$_{20}$class of compounds.

Two-stage multipolar ordering in Pr(TM)$_2$Al$_{20}$ Kondo materials