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The strong mixing of close levels with two valence electrons in Be-like xenon greatly complicates ab initio QED calculations beyond the first-order approximation. Because of a strong interplay between the electron-electron correlation and QED effects, the standard single-level perturbative QED approach may fail, even if it takes into account the second-order screened QED diagrams. In the present Letter, the corresponding obstacles are overcome by working out the QED perturbation theory for quasidegenerate states. The contributions of all