  Many standard model extensions that address the hierarchy problem contain
Dirac-fermion partners of the top quark, which are typically expected around
the TeV scale. Searches for these vector-like quarks mostly focus on their
decay into electroweak gauge bosons and Higgs plus a standard model quark. In
this article, backed by models of composite Higgs, we propose a set of
simplified scenarios, with effective Lagrangians and benchmarks, that include
more exotic decay channels, which modify the search strategies and affect the
bounds. Analysing several classes of underlying models, we show that exotic
decays are the norm and commonly appear with significant rates. All these
models contain light new scalars that couple to top partners with charge $5/3$,
$2/3$, and $-1/3$.
