Using exact-diagonalization techniques supplemented by a Dyson equation embedding procedure, the transport properties of multilevel quantum dots are investigated in the Kondo regime. The conductance can be decomposed into the contributions of each level. It is shown that these channels can carry a different phase, and destructive interference processes are observed when the phase difference between them is $\pmπ$. This effect is very different from those observed in bulk metals with magnetic impurities, where the phase differences play no significant role. The effect is also different from other recent studies of interference processes in dots, as discussed in the text. In particular, no external magnetic field is here introduced, and the hopping amplitudes dot-leads for all levels are the same. However, conductance cancellations induced by interactions are still observed. Another interesting effect reported here is the formation of localized states that do not participate in the transport. When one of these states crosses the Fermi level, the electronic occupation of the quantum dot changes, modifying the many-body physics of the system and indirectly affecting the transport properties. Novel discontinuities between two finite conductance values can occur as the gate voltage is varied, as discussed here.