Katharine McPhee can't keep her hands off her co-workers ... but it's not a director this time ... it's her new show's leading man. McPhee was on set Thursday getting handsy with Elyes Gabel , her co-star in the upcoming CBS series, "Scorpion."

Gabel's not married and she's getting divorced. You'll remember ... photos surfaced of McPhee locking lips with " Smash " director Michael Morris in October 2013. McPhee was married to Nick Cokas (though she claims they were separated ) and Morris was married to actress Mary McCormack (they're still together ).