This work addresses Riemann–Hilbert boundary value problems (RHBVPs) for null solutions to iterated perturbed Dirac operators over biaxially symmetric domains in \(\mathbb {R}^n\) with Clifford-algebra-valued variable coefficients. We first resolve the unperturbed case of poly-monogenic functions, i.e., null solutions to iterated Dirac operators, by constructing explicit solutions via a biaxially adapted Almansi-type decomposition, which decouples hierarchical structures through recursive integral operators. Then, generalizing to vector wave number-perturbed iterated Dirac operators, we extend the decomposition to manage spectral anisotropy while preserving symmetry constraints, ensuring regularity under Clifford-algebraic parameterizations. As a key application, closed-form solutions to the Schwarz problem are derived, demonstrating unified results across classical and higher-dimensional settings. The interplay of symmetry, decomposition, and perturbation theory establishes a cohesive framework for higher-order boundary value challenges in Clifford analysis.
