  At zero temperature, the Landauer formalism combined with static density
functional theory is able to correctly reproduce the Kondo plateau in the
conductance of the Anderson impurity model provided that an
exchange-correlation potential is used which correctly exhibits steps at
integer occupation. Here we extend this recent finding to multi-level quantum
dots described by the constant-interaction model. We derive the exact
exchange-correlation potential in this model for the isolated dot and deduce an
accurate approximation for the case when the dot is weakly coupled to two
leads. We show that at zero temperature and for non-degenerate levels in the
dot we correctly obtain the conductance plateau for any odd number of electrons
on the dot. We also analyze the case when some of the levels of the dot are
degenerate and again obtain good qualitative agreement with results obtained
with alternative methods. As in the case of a single level, for temperatures
larger than the Kondo temperature, the Kohn-Sham conductance fails to reproduce
the typical Coulomb blockade peaks. This is attributed to {\em dynamical}
exchange-correlation corrections to the conductance originating from
time-dependent density functional theory.
