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As is known, any realization of SU(2) in the phase space of a dynamicalsystem can be generalized to accommodate the exceptional supergroup$D(2,1;\alpha)$, which is the most general $\mathcal{N}{=}\,4$ supersymmetricextension of the conformal group in one spatial dimension. We construct novelspinning extensions of $D(2,1;\alpha)$ superconformal mechanics by adjustingthe SU(2) generators associated with the relativistic spinning particle coupledto a spherically symmetric Einstein-Maxwell background. The angular sector ofthe full superconformal system corresponds to the orbital motion of a particlecoupled to a symmetric Euler top, which represents the spin degrees of freedom.This particle moves either on the two-sphere, optionally in the external fieldof a Dirac monopole, or in the SU(2) group manifold. Each case is proven to besuperintegrable, and explicit solutions are given.

Spinning extensions of $D(2,1;\alpha)$ superconformal mechanics