The electronic structure of single-crystal PuO${}_{2}$ is studied using O $1s$ x-ray absorption (XA) and x-ray emission. Interpretation of the experimental data is supported by extensive first-principles calculations on the basis of the $\mathrm{density}\mathrm{ }\mathrm{functional}\mathrm{ }\mathrm{theory}+U$ approach. The measured XA spectra show a significant difference in intensity for the first two peaks between different spots or areas on the single crystal. Our theoretical simulations show that the first peak, at $~$531 eV, can be attributed to O $2p$-Pu 5$f$ hybridization, while the second peak, at $~$533.4 eV, is due to hybridization of O 2$p$ with Pu $d$ states. The reasons for the observed differences in the O $1s$ XA spectra are explored by calculating a number of defect structures PuO${}_{2\ifmmode\pm\else\textpm\fi{}x}$ as well as by simulating the existence of Pu(V) sites. Our results indicate the presence of oxidation states higher than Pu(IV) in some areas of the single crystal. The findings also suggest that plutonium oxide with a Pu fraction in an oxidation state higher than Pu(IV) consists of inequivalent Pu sites with Pu${}^{(\mathrm{IV})}$O${}_{2}$ and Pu${}^{(\mathrm{V})}$O${}_{2}$ rather than representing a system where the Pu oxidation state is constantly fluctuating between Pu(IV) and Pu(V).