For Pete's sake, why?
Hasn't Doumit already done this? Offensively, Doumit was vastly better than Cota overall. In fact, Doumit's OPS put him well above the major league average for catchers. He's younger than Cota and has a lot more upside.
Cota, for all his clutch-whatever-ness, is a bad offensive player who never showed much promise with the bat in the high minors and will be 27 next year. Whatever Cota's skills on defense, Doumit is the future there, and he needs time to learn the position. Cota had a dreadful 623 OPS against righties last year. Catchers need time off, so the catcher position is always a time-share to a certain extent, but if Doumit stays healthy and doesn't catch 120 or 130 games next year, that's a mistake.