Can One have Significant Deviations from Leptonic $3\times 3$ Unitarity in the Framework of Type I Seesaw Mechanism?

We address the question of deviations from $3\times 3$ unitarity of the leptonic mixing matrix showing that, contrary to conventional wisdom, one may have significant deviations from unitarity in the framework of type I seesaw mechanism. In order for this scenario to be feasible, at least one of the heavy neutrinos must have a mass at the TeV scale, while the other two may have much larger masses. We present specific examples where deviations from $3\times 3$ unitarity are sufficiently small to conform to all the present stringent experimental bounds but are sufficiently large to have the potential for being detectable at the next round of experiments.