  We introduce a family of commuting generalised symmetries of the Dunkl--Dirac
operator inspired by the Maxwell construction in harmonic analysis. We use
these generalised symmetries to construct bases of the polynomial
null-solutions of the Dunkl--Dirac operator. These polynomial spaces form
representation spaces of the Dunkl--Dirac symmetry algebra. For the
$\mathbb{Z}_2^d$ case, the results are compared with previous investigations.
