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In our recent paper, we have investigated the potential for the LHC to discover vector-like quark partner states singly produced via their chromomagnetic moment interactions. These production mechanisms extend traditional searches which rely on pair-production of top-quark partner states or on the single production of these states through electroweak interactions, in the sense of providing greatly increased reach in parameter space regions where traditional searches are insensitive. In this study we determine the potential of both the 14 TeV high-luminosity LHC (HL-LHC) and a 100 TeV proton-proton collider to probe new vector-like quarks produced in this mode. We focus on the single production of a top-quark partner in association with an ordinary top-quark, as well as on the resonant production of the bottom-quark partner with its subsequent decay to a top-quark partner and a W boson. For both cases we consider a top-partner decay to the Higgs boson and an ordinary top-quark. We find that HL-LHC and a future 100 TeV proton collider can probe vector-like partner masses up to about 3 TeV and 15-20 TeV respectively, visibly extending the range of the traditional vector like quark partner searches.