  We analyse the general structure of the three-point functions involving
conserved higher-spin currents $J_{s} := J_{\alpha(i) \dot{\alpha}(j)}$
belonging to any Lorentz representation in four-dimensional conformal field
theory. Using the constraints of conformal symmetry and conservation equations,
we computationally analyse the general structure of three-point functions
$\langle J^{}_{s_{1}} J'_{s_{2}} J''_{s_{3}} \rangle$ for arbitrary spins and
propose a classification of the results. For bosonic vector-like currents with
$i=j$, it is known that the number of independent conserved structures is $2
\min (s_{i}) + 1$. For the three-point functions of conserved currents with
arbitrarily many dotted and undotted indices, we show that in many cases the
number of structures deviates from $2 \min (s_{i}) + 1$.
