The existence of new vector-like quarks is often predicted by models of new physics beyond the Standard Model, and the development of discovery strategies at colliders is the object of an intense effort from the high-energy community. Our analysis aims at identifying the constraints on and peculiar signatures of simplified scenarios containing textit{two} vector-like quark doublets mixing with textit{any} of the SM quark generations. This scenario is a necessary ingredient of a broad class of theoretically motivated constructions. We focus on the two charge $2/3$ states $t_{1,2}^prime$ that, due to their peculiar mixing patterns, feature new production and decay modes that are not searched for at the LHC: single production of the heavier state can dominate over the light one, while pair production via electroweak interactions overcomes the QCD one for masses at the TeV scale.
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