We explore the phenomenology of models containing one Vector-Like Quark (VLQ), , which can decay into the Standard Model (SM) top quark, , and a new spin-0 neutral boson, , the latter being either a scalar or pseudoscalar state. We parametrise the underlying interactions in terms of a simplified model which enables us to capture possible Beyond the SM (BSM) scenarios. We discuss in particular three such scenarios: one where the SM state is supplemented by an additional scalar, one which builds upon a 2-Higgs Doublet Model (2HDM) framework and another which realises a Composite Higgs Model (CHM) through partial compositeness. Such exotic decays of the can be competitive with decays into SM particles, leading to new possible discovery channels at the Large Hadron Collider (LHC). Assuming pair production via strong interactions, we design signal regions optimised for one transition (while being inclusive on the other $$ \overline{t} $$ decay, and vice versa), followed by the decay of into the two very clean experimental signatures and ( ) . We perform a dedicated signal- to-background analysis in both channels, by using Monte Carlo (MC) event simulations modelling the dynamics from the proton-proton to the detector level. Under the assumption of BR( ) = 100%, we are therefore able to realistically quantify the sensitivity of the LHC to both the and masses, assuming both current and foreseen luminosities. This approach paves the way for the LHC experiments to surpass current VLQ search strategies based solely on decays into SM bosons ( , ).