  In 4d $\mathcal{N}=1$ superconformal field theories (SCFTs) the R-symmetry
current, the stress-energy tensor, and the supersymmetry currents are grouped
into a single object, the Ferrara-Zumino multiplet. In this work we study the
most general form of three-point functions involving two Ferrara-Zumino
multiplets and a third generic multiplet. We solve the constraints imposed by
conservation in superspace and show that non-trivial solutions can only be
found if the third multiplet is R-neutral and transforms in suitable Lorentz
representations. In the process we give a prescription for counting independent
tensor structures in superconformal three-point functions. Finally, we set the
Grassmann coordinates of the Ferrara-Zumino multiplets to zero and extract all
three-point functions involving two R-currents and a third conformal primary.
Our results pave the way for bootstrapping the correlation function of four
R-currents in 4d $\mathcal{N}=1$ SCFTs.
