  We study an extended SU(N) single-impurity Kondo model in which the impurity
spin is described by a combination of Abrikosov fermions and Schwinger bosons.
Our aim is to describe both the quasiparticle-like excitations and the locally
critical modes observed in various physical situations, including non-Fermi
liquid (NFL) behavior in heavy fermions in the vicinity of a quantum critical
point and anomalous transport properties in quantum wires. In contrast with
models with either pure bosonic or pure fermionic impurities, the strong
coupling fixed point is unstable against the conduction electron kinetic term
under certain conditions. The stability region of the strong coupling fixed
point coincides with the region where the partially screened, effective
impurity repels the electrons on adjacent sites. In the instability region, the
impurity tends to attract $(N-1)$ electrons to the neighboring sites, giving
rise to a double-stage Kondo effect with additional screening of the impurity.
