  We present a microscopic Fermi-liquid view on the low-energy transport
through an Anderson impurity with $N$ discrete levels, at arbitrary electron
filling $N_d$. It is applied to nonequilibrium current fluctuations, for which
the two-quasiparticle collision integral and the three-body correlations that
determine the quasiparticle energy shift play important roles. Using the
numerical renormalization group up to $N=6$, we find that for strong
interactions the three-body fluctuations are determined by a single parameter
other than the Kondo energy scale in a wide filling range $1 \lesssim N_d
\lesssim N-1$. It significantly affects the current noise for $N>2$ and the
behavior of noise in magnetic fields.
