The Yankees shouldn't put all their eggs in the Gerrit Cole basket ... because it's gonna take more than one star pitcher to make NY a legit contender, so says Johnny Damon.

Of course, the Yankees are trying like hell to sign the former Houston Astros star -- they reportedly sent everyone from GM Brian Cashman to Yanks legend Andy Pettitte to California this week to meet with the free agent.

29-year-old Cole was a STUD in 2019 -- finishing 2nd in a CLOSE Cy Young race to his teammate, Justin Verlander.