  Motivated by recent studies of superconformal mechanics extended by spin
degrees of freedom, we construct minimally superintegrable models of spinning
particles on 2-sphere, the spin degrees of freedom of which are represented by
a 3-vector obeying the structure relations of a 3d real Lie algebra.
Generalisations involving an external field of the Dirac monopole, or the
motion on the group manifold of SU(2), or a scalar potential giving rise to two
quadratic constants of the motion are discussed. A procedure how to build
similar extensions, which rely upon d=4,5,6 real Lie algebras, is elucidated.
