  As a continuation of a previous work [B. Horv\'ath et al., Phys. Rev. B {\bf
82}, 165129 (2010)], here we extend the so-called Fluctuation Exchange
Approximation (FLEX) to study the non-equilibrium singlet-triplet transition.
We show that, while being relatively fast and a conserving approximation, FLEX
is able to recover all important features of the transition, including the
evolution of the linear conductance throughout the transition, the two-stage
Kondo effect on the triplet side, and the gradual opening of the
singlet-triplet gap on the triplet side of the transition. A comparison with
numerical renormalization group calculations also shows that FLEX captures
rather well the width of the Kondo resonance. FLEX thus offers a viable route
to describe correlated multi-level systems under non-equilibrium conditions,
and, in its rather general form, as formulated here, it could find a broad
application in molecular electronics calculations.
