  Dynamical realizations of the most general N=4 superconformal group in one
dimension D(2,1;a) are reconsidered from the perspective of the R-symmetry
subgroup SU(2). It is shown that any realization of the R-symmetry subalgebra
in some phase space can be extended to a representation of the Lie superalgebra
corresponding to D(2,1;a). Novel couplings of arbitrary number of
supermultiplets of the type (1,4,3) and (0,4,4) with a single supermultiplet of
either the type (3,4,1), or (4,4,0) are constructed. D(2,1;a) superconformal
mechanics describing superparticles propagating near the horizon of the extreme
Reissner-Nordstrom-AdS-dS black hole in four and five dimensions is considered.
The parameter a is linked to the cosmological constant.
