  Extensions of the Standard Model that include vector-like quarks commonly
also include additional particles that may mediate new production or decay
modes. Using as example the minimal linear $\sigma$ model, that reduces to the
minimal $SO(5)/SO(4)$ composite Higgs model in a specific limit, we consider
the phenomenology of vector-like quarks when a scalar singlet $\sigma$ is
present. This new particle may be produced in the decays $T \to t \sigma$, $B
\to b \sigma$, where $T$ and $B$ are vector-like quarks of charges $2/3$ and
$-1/3$, respectively, with subsequent decay $\sigma \to W^+ W^-, ZZ, hh$. By
scanning over the allowed parameter space we find that these decays may be
dominant. In addition, we find that the presence of several new particles
allows for single $T$ production cross sections larger than those expected in
minimal models. We discuss the observability of these new signatures in
existing searches.
