  We show that it is possible to accommodate the observed size of the phase in
$B^0_s$--$\bar B^0_s$, mixing in the framework of a model with violation of
$3\times 3$ unitarity. This violation is associated to the presence of a new
$Q=2/3$ isosinglet quark $T$, which mixes both with $t$ and $c$ and has a mass
not exceeding 500 GeV. The crucial point is the fact that this framework allows
for $\chi\equiv\arg(-V_{ts}V_{cb}V_{tb}^*V_{cs}^*)$ of order $\lambda$, to be
contrasted with the situation in the Standard Model, where $\chi$ is
constrained to be of order $\lambda^2$. We point out that this scenario implies
rare top decays $t\to cZ$ at a rate observable at the LHC and $|V_{tb}|$
significantly different from unity. In this framework, one may also account for
the observed size of $D^0$--$\bar D^0$ mixing without having to invoke long
distance contributions. It is also shown that in the present scenario, the
observed size of $D^0$--$\bar D^0$ mixing constrains
$\chi^\prime\equiv\arg(-V_{cd}V_{us}V_{cs}^*V_{ud}^*)$ to be of order
$\lambda^4$, which is significantly smaller than what is allowed in generic
models with violations of $3\times 3$ unitarity.
