  We analyze the transport properties of a double quantum dot device in the
side-coupled configuration. A small quantum dot (QD), having a single relevant
electronic level, is coupled to source and drain electrodes. A larger QD, whose
multilevel nature is considered, is tunnel-coupled to the small QD. A Fermi
liquid analysis shows that the low temperature conductance of the device is
determined by the total electronic occupation of the double QD. When the small
dot is in the Kondo regime, an even number of electrons in the large dot leads
to a conductance that reaches the unitary limit, while for an odd number of
electrons a two stage Kondo effect is observed and the conductance is strongly
suppressed. The Kondo temperature of the second stage Kondo effect is strongly
affected by the multilevel structure of the large QD. For increasing level
spacing, a crossover from a large Kondo temperature regime to a small Kondo
temperature regime is obtained when the level spacing becomes of the order of
the large Kondo temperature.
