  We consider a four dimensional generalized Wess-Zumino model formulated in
terms of an arbitrary K\"{a}hler potential $\mathcal{K}(\Phi,\bar{\Phi})$ and
an arbitrary chiral superpotential $\mathcal{W}(\Phi)$. A general analysis is
given to describe the possible interactions of this theory with external higher
spin gauge superfields of the ($s+1,s+1/2$) supermultiplet via higher spin
supercurrents. It is shown that such interactions do not exist beyond
supergravity $(s\geq2)$ for any $\mathcal{K}$ and $\mathcal{W}$. However, we
find three exceptions, the theory of a free massless chiral, the theory of a
free massive chiral and the theory of a free chiral with linear superpotential.
For the first two, the higher spin supercurrents are known and for the third
one we provide the explicit expressions. We also discuss the lower spin
supercurrents. As expected, a coupling to (non-minimal) supergravity ($s=1$)
can always be found and we give the generating supercurrent and supertrace for
arbitrary $\mathcal{K}$ and $\mathcal{W}$. On the other hand, coupling to the
vector supermultiplet ($s=0$) is possible only if
$\mathcal{K}=\mathcal{K}(\bar{\Phi}\Phi)$ and $\mathcal{W}=0$.
