  We resonantly excite the $K$ series of O$^{5+}$ and O$^{6+}$ up to principal
quantum number $n=11$ with monochromatic x rays, producing $K$-shell holes, and
observe their relaxation by soft-x-ray emission. Some photoabsorption
resonances of O$^{5+}$ reveal strong two-electron--one-photon (TEOP)
transitions. We find that for the $[(1s\,2s)_1\,5p_{3/2}]_{3/2;1/2}$ states,
TEOP relaxation is by far stronger than the radiative decay and competes with
the usually much faster Auger decay path. This enhanced TEOP decay arises from
a strong correlation with the near-degenerate upper states
$[(1s\,2p_{3/2})_1\,4s]_{3/2;1/2}$ of a Li-like satellite blend of the He-like
$K\alpha$ transition. Even in three-electron systems, TEOP transitions can play
a dominant role, and the present results should guide further research on the
ubiquitous and abundant many-electron ions where electronic energy degeneracies
are far more common and configuration mixing is stronger.
