  For SCFTs with an $SU(2)$ R-symmetry, we determine the superconformal blocks
that contribute to the four-point correlation function of a priori distinct
half-BPS superconformal primaries as an expansion in terms of the relevant
bosonic conformal blocks. This is achieved by using the superconformal Casimir
equation and the superconformal Ward identity to fix the coefficients of the
bosonic blocks uniquely in a dimension-independent way. In addition we find
that many of the resulting coefficients are related through a web of linear
transformations of the conformal data.
