Quantum dots and single-molecule transistors may exhibit level crossings induced by tuning external parameters such as magnetic eld or gate voltage. For Coulomb blockaded devices, this shows up as an inelastic cotunneling threshold in the dierential conductance, which can be tuned to zero at the crossing. Here we show that, in addition, level crossings can give rise to a nearly vertical
step-edge, ridge or even a Fano-like ridge-valley feature in the dierential conductance inside the relevant Coulomb diamond. We study a gate-tunable quasidegeneracy between singlet and triplet ground states, and demonstrate how these dierent shapes may result from a competition between nonequilibrium occupations and weak (spin-orbit) mixing of the states. Our results are shown to be in qualitative agreement with recent transport measurements on a Mn complex [E. A. Osorio et al., Nano Lett 10, 105 (2010)]. The eect remains entirely general and should be observable in a wide range of Coulomb blockaded devices.