  In our recent work\cite{Noh:2023zoq}, the mass and binding energy of $T_{cc}$
are found to be $3873$ MeV and $-2$ MeV, respectively, which align with the
observations reported at LHCb\cite{LHCb:2021vvq}. Based on our latest quark
model approach, we extend our search for other potentially stable
configurations of doubly heavy tetraquarks using our nonrelativistic quark
model described in Ref.~\cite{Noh:2023zoq}. Our numerical calculations indicate
that the $\bar{u}\bar{s}cb$ configuration is deeply bound. However, the
$\bar{u}\bar{d}cb$ configuration with the isospin symmetry in the light quark
sector is relatively less bound. In this study, we emphasize a compulsory
aspect for requiring a complete set of three dimensional harmonic oscillator
bases through the discussion of the $\bar{u}\bar{s}cb$ configuration and
investigate the essential differences between the $\bar{u}\bar{s}cb$ and
$\bar{u}\bar{d}cb$ configurations.
