  Self-dual gauge potentials admit supersymmetric couplings to higher-spin
fields satisfying interacting forms of the first order Dirac--Fierz equation.
The interactions are governed by conserved currents determined by
supersymmetry. These super-self-dual Yang-Mills systems provide on-shell
supermultiplets of arbitrarily extended super-Poincar\'e algebras; classical
consistency not setting any limit on the extension N. We explicitly display
equations of motion up to the $N=6$ extension. The stress tensor, which
vanishes for the $N\le 3$ self-duality equations, not only gets resurrected
when $N=4$, but is then a member of a conserved multiplet of gauge-invariant
tensors.
