<p>Despite the unprecedented success achieved by Kohn-Sham density functional theory (KS-DFT) in the past few decades, the standard approximations used for the KS exchange-correlation functional typically lead to unacceptably large errors when applied to strongly-correlated electronic systems. Partition-DFT (P-DFT) is a formally exact reformulation of KS-DFT in which the ground-state density and energy of a system are obtained through self-consistent calculations on isolated fragments, with a partition energy introduced to account for the inter-fragment interactions. The unique advantage of this partitioning scheme lies in the fact that it adopts the electron density of fragments as the main variable, in place of the density of the entire system in KS-DFT, so that novel approximations can be constructed in terms of fragment properties. With a simple overlap approximation (OA) of the partition energy proposed for binary-partitioned systems, P-DFT is able to rectify the static correlation error caused by standard density functional approximations for strongly-correlated diatomic molecules. In this work, we first implement P-DFT on a one-dimensional (1D) real-space grid and calculate the ground-state energy and density of a series of 1D hydrogen chains using the local density approximation (LDA) as the density functional approximation for fragments. We then propose the generalized overlap approximation (GOA) and the corrected generalized overlap approximation (cGOA), which extends the applicability of OA to systems partitioned into more than two fragments. Combining LDA with cGOA leads to quantitatively correct dissociation curves of hydrogen chains. The static correlation error of LDA is suppressed by cGOA in the strongly-correlation regime when the calculations are performed in a spin-restricted manner, i.e., without the spin symmetry breaking. Additionally, GOA induces an improvement of the ground-state density upon LDA results, and hence helps P-DFT provide a better description of the density dimerization in hydrogen chains.</p>