We consider a quantum dot with ${cal K}{geq} 2$ orbital levels occupied by two electrons connected to two electric terminals. The generic model is given by a multi-level Anderson Hamiltonian. The weak-coupling theory at the particle-hole symmetric point is governed by a two-channel $S{=}1$ Kondo model characterized by intrinsic channels asymmetry. Based on a conformal field theory approach we derived an effective Hamiltonian at a strong-coupling fixed point. The Hamiltonian capturing the low-energy physics of a two-stage Kondo screening represents the quantum impurity by a two-color local Fermi-liquid. Using non-equilibrium (Keldysh) perturbation theory around the strong-coupling fixed point we analyze the transport properties of the model at finite temperature, Zeeman magnetic field and source-drain voltage applied across the quantum dot. We compute the Fermi-liquid transport constants and discuss different universality classes associated with emergent symmetries.
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