  We investigate the quantum transport through Kondo impurity assuming both a
large number of orbital channels $\mathcal K$$\gg $$1$ for the itinerant
electrons and a semi-classical spin ${\cal S}$ $\gg $ $1$ for the impurity. The
non-Fermi liquid regime of the Kondo problem is achieved in the overscreened
sector $\mathcal K>2\mathcal{S}$. We show that there exist two distinct
semiclassical regimes for the quantum transport through impurity: i) $\mathcal
K$ $\gg$ $\mathcal S$ $\gg$ $1$, differential conductance vanishes and ii)
$\mathcal S$$/$$\mathcal K{=}\mathcal C$ with $ 0$$<$$\mathcal C$$<$$1/2$,
differential conductance reaches some non-vanishing fraction of its unitary
value. Using conformal field theory approach we analyze behavior of the quantum
transport observables and residual entropy in both semiclassical regimes. We
show that the semiclassical limit ii) preserves the key features of resonance
scattering and the most essential fingerprints of the non-Fermi liquid
behavior. We discuss possible realization of two semiclassical regimes in
semiconductor quantum transport experiments.
