In a previous paper [R. Baumert, I. Broser, J. Gutowski, and A. Hoffman, Phys. Rev. B 27, 6263 (1983)] it has been shown that high-density, high-resolution excitation spectroscopy gives new information on the electronic and vibronic excited states of the acceptor--bound-exciton complex (${A}^{0}$,${X}_{A}$) with two holes from the A valence band in CdS. We now report on corresponding results for the (${A}^{0}$,${X}_{B}$) configuration which includes one hole from the second B valence band. This complex is unstable for a very fast B\ensuremath{\rightarrow}A hole conversion, and therefore gives rise to a set of excitation resonances of the ${I}_{1}$ luminescence arising from the (${A}^{0}$,${X}_{A}$) recombination. A detailed theoretical analysis of the energetic structure of the (${A}^{0}$,${X}_{B}$) complex including the dependence on the excitation intensity and on an applied magnetic field allows the correct assignment of the excitation resonances to the (${A}^{0}$,${X}_{B}$) fine-structure levels originating from the interparticle-exchange interactions. It is shown that the magnetic field is a suitable means of distinguishing the different (${A}^{0}$,${X}_{B}$) ground-state levels. The magnetic field also creates allowed transitions which are dipole forbidden in the zero-field case. A self-contained model of the (${A}^{0}$,${X}_{B}$) complex thus can be developed, including all symmetry states and yielding adequate values for the exchange energies within the complex.