  The noncrossing approximation (NCA) is generalized to the multi-channel
Kondo-spin Hamiltonian with arbitrary anisotropic exchange couplings and an
external magnetic field, and applied -- in the framework of Matveev's mapping
-- to the charge fluctuations in a single-electron box at the Coulomb blockade.
The temperature dependences of the charge step and the capacitance are
calculated for a narrow point contact. At low temperatures and close to the
degeneracy point, the capacitance line shape exhibits an approximate scaling
with U/\sqrt{T}, where U is the deviation in gate voltage from the degeneracy
point. This scaling relation is proposed as a sharp experimental diagnostic for
the non-Fermi-liquid physics of the system at low temperatures. Both the
reliability and shortcomings of the Kondo NCA are discussed in detail. Through
comparison with poor-man's scaling, we are able to pinpoint the omission of
particle-particle processes as the origin of the NCA flaws. An extended
diagrammatic scheme is devised to amend the NCA flaws.
