As is known, any realization of SU(2) in the phase space of a dynamical sys-tem can be generalized to accommodate the exceptional supergroupD(2;1;α), which isthe most generalN= 4 supersymmetric extension of the conformal group in one spatialdimension. We construct novel spinning extensions ofD(2;1;α) superconformal mechanicsby adjusting the SU(2) generators associated with the relativistic spinning particle coupledto a spherically symmetric Einstein-Maxwell background. The angular sector of the fullsuperconformal system corresponds to the orbital motion of a particle coupled to a sym-metric Euler top, which represents the spin degrees of freedom. This particle moves eitheron the two-sphere, optionally in the external eld of a Dirac monopole, or in the SU(2)group manifold. Each case is proven to be superintegrable, and explicit solutions are given.