  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. Due to 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 the Feynman diagrams up to the second order are taken into
account. The many-electron QED effects are rigorously evaluated in the
framework of the extended Furry picture to all orders in the nuclear-strength
parameter $\alpha Z$. The higher-order electron-correlation effects are
considered within the Breit approximation. The nuclear recoil effect is
accounted for as well. The developed approach is applied to high-precision QED
calculations of the ground and singly excited energy levels in Be-like xenon.
The most accurate theoretical predictions for the binding and excitation
energies are obtained. These results deviate from the most precise experimental
value by $3\sigma$ but perfectly agree with a more recent measurement.
