In this talk, we will discuss Toeplitz operators on the Hardy space over the polydisc. In particular, we are interested in the classification of partially isometric Toeplitz operators. Such a classification was first studied by A. Brown and R. G. Douglas, in the case of Hardy space over the disc, by exploiting the celebrated Beurling-Lax-Halmos(BLH) theorem. Though the absence of BLH-type result in higher dimensions presents an obvious obstruction, yet we will present a satisfactory and novel generalization of Brown-Douglas theorem. This talk is based on a joint work with Deepak K.D. and J. Sarkar.