  We calculate the nonlinear cotunneling conductance through a quantum dot with
3 electrons occupying the three highest lying energy levels. Starting from a
3-orbital Anderson model, we apply a generalized Schrieffer-Wolff
transformation to derive an effective Kondo model for the system. Within this
model we calculate the nonequilibrium occupation numbers and the corresponding
cotunneling current to leading order in the exchange couplings. We identify the
inelastic cotunneling thresholds and their splittings with applied magnetic
field, and make a qualitative comparison to recent experimental data on carbon
nanotube and InAs quantum-wire quantum dots. Further predictions of the model
like cascade resonances and a magnetic-field dependence of the orbital level
splitting are not yet observed but within reach of recent experimental work on
carbon nanotube and InAs nanowire quantum dots.
