Most limits on the fourth generation heavy top quark (the t ) are based on the assumed dominance of t → W b, which is expected to be case in the minimal fourth generation framework with a single Higgs (the so called SM4). Here we show, within a variant of a Two Higgs Doublet Model with four generations of fermions, that, in general, a different t detection strategy is required if the physics that underlies the new heavy fermionic degrees of freedom goes beyond the "naive" SM4. We find that the recent CMS lower bounds: m t < 450 GeV in the semi-leptonic channel pp → t t → νbqqb and m t < 557 GeV in the dilepton channel pp → t t → + − ννbb, that were obtained using the customary (SM4-driven) detection strategies, do not apply.In particular, we demonstrate that if the decay t → ht dominates, then applying the "standard" CMS search tools leads to a considerably relaxed lower bound: m t > ∼ 350 GeV. We, therefore, suggest an alternative search strategy that is more sensitive to beyond SM4 dynamics of the fourth generation fermions.