  In this paper, we study partially isometric Toeplitz operators $T_{\Phi}$ on
Hilbert space-valued Hardy spaces $H_{\mathcal{E}}^2(\mathbb{D}^n)$ over the
unit polydisc. We establish the following crucial phenomenon: the range of
partially isometric Toeplitz operators is always a Beurling-type invariant
subspace of $H_{\mathcal{E}}^2(\mathbb{D}^n)$. Using this result, we prove that
partially isometric Toeplitz operators always admit the following
factorization: \[ T_{\Phi} = M_{\Gamma} M_{\Psi}^*, \] where
$\Gamma(\boldsymbol{z}), \Psi(\boldsymbol{z})$ are operator-valued inner
functions on $\mathbb{D}^n$, governed by certain conditions that force
$M_{\Gamma} M_{\Psi}^*$ to become a Toeplitz operator. Our results are new even
in the case of Hardy spaces over the unit disc, and extend the work of
Brown-Douglas, Deepak-Pradhan-Sarkar on scalar-valued Hardy spaces.
