Provided herein is an electrodialysis metathesis system that has at least one stack or quad of compartments arranged so each compartment is in fluid communication with its adjacent compartment via alternating cation- and anion-exchange membranes. The compartments in a stack are a feed compartment, a substitution salt solution compartment, a first concentrated compartment and a second concentrated compartment. Also provided are processes and methods for separating or recovering a metal, for example, a rare earth element, or a salt or a combination thereof from a salt-containing water. Simultaneous metathesis reactions and electrodialysis across the stack recovers one or more metal or salts from the salt-containing water which desalinates the salt-containing water.