Brackish water/seawater reverse osmosis (RO) desalination is a key solution to global freshwater scarcity. However, the water recovery ($R_w$) in conventional RO desalination plants is limited by the operating pressure ($∆P$). As a novel staged RO technology, low-salt-rejection RO (LSRRO) can potentially enhance the $R_w$ in the desalination plants. In this study, we perform process modeling and techno-economic analysis to evaluate the viability of upgrading current RO desalination plants with LSRRO. Based on the results from process modeling, in typical brackish water RO (BWRO) and seawater RO (SWRO) desalination plants, adding an LSRRO stage can effectively enhance the $R_w$ by 21 and 53 %, respectively, and the energy efficiencies are not compromised with the enhanced $R_w$. From techno-economic analysis, upgrading RO desalination plant with LSRRO is highly viable. Specifically, after adding an LSRRO stage in a BWRO plant, the $R_w$ can be enhanced from 71 to 81 % without notably increasing the levelized cost of water ($\mathit{LCOW}$), and adding an LSRRO stage in the SWRO plant with zero brine discharge can reduce the $\mathit{LCOW}$ by 30 %. The findings in our study highlight the vast potential of adopting LSRRO in brackish water/seawater desalination plants, and shed lights on the design of future desalination plants.