  Degenerate perturbation theory from quantum mechanics is inadequate in
density functional theory (DFT) because of nonlinearity in the Kohn-Sham
potential. Herein, we develop the fully general perturbation theory for
open-shell, degenerate systems in Kohn-Sham DFT, without assuming the presence
of symmetry or equal occupation of degenerate orbitals. To demonstrate the
resulting methodology, we apply it to the iron atom in the central field
approximation, perturbed by an electric quadrupole. This system was chosen
because it displays both symmetry required degeneracy, between the five
3\textit{d} orbitals, as well as accidental degeneracy, between the 3\textit{d}
and 4\textit{s} orbitals. The quadrupole potential couples the degenerate
3\textit{d} and 4\textit{s} states, serving as an example of the most general
perturbation.
