  We calculate the spectral density and occupations of a system of two
capacitively coupled quantum dots, each one connected to its own pair of
conducting leads, in a regime of parameters in which the total coupling to the
leads for each dot $\Gamma_i$ are different. The system has been used recently
to perform pseudospin spectroscopy by controlling independently the voltages of
the four leads. For an odd number of electrons in the system,
$\Gamma_1=\Gamma_2$, equal dot levels $E_1=E_2$ and sufficiently large interdot
repulsion $U_{12}$ the system lies in the SU(4) symmetric point of spin and
pseudospin degeneracy in the Kondo regime. In the more realistic case $\Gamma_1
\neq \Gamma_2$, pseudospin degeneracy is broken and the symmetry is reduced to
SU(2). Nevertheless we find that the essential features of the SU(4) symmetric
case are recovered by appropriately tuning the level difference
$\delta=E_2-E_1$. The system behaves as an SU(4) Kondo one at low energies. Our
results are relevant for experiments which look for signatures of SU(4)
symmetry in the Kondo regime of similar systems.
