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 exchangecorrelation 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 dynamical exchangecorrelation corrections to the conductance originating from time-dependent density functional theory.Copyright line will be provided by the publisher 1 Introduction Common wisdom has it that Density Functional Theory (DFT) is not able to describe strongly correlated systems although the fundamental theorems of DFT apply to these systems as well. In fact, the difficulties of dealing with strong correlations are not inherent to DFT but to the DFT approximations. In the last years there has been considerable progress in understanding which features a DFT approximation should have in order to capture strong correlation effects [1][2][3][4][5][6][7][8][9][10][11][12][13], and the derivative discontinuity of the exchange-correlation energy functional [14] has emerged as one of the key properties. In the context of quantum transport the derivative discontinuity turned out to be crucial to reproduce the conductance plateau [15][16][17] due to the Kondo effect, a hallmark of strong correlations.