Does the relationship need to be official/mutual or does the FL having a one-sided crush on someone else count? And does it matter if it isn't 100% a romance show?
I would recommend:
Story of Yanxi Palace - 2ML (the emperor) is interested in the FL. FL would rather die than give up on her relationship with ML, but ML would rather give up on their relationship so FL can live. FL treats ML's decision as a betrayal and gives up on ML to get together with 2ML. Eventually I guess FL does fall in love with 2ML but it's quite iffy given the power dynamics (I mean, he's the emperor).
Strong Woman Do Bong Soon - FL was interested in 2ML at the start, and 2ML was interested in her as well but he didn't show it. He only acted on his feelings when ML came into the picture, which was of course, too late.
Love Between Fairy and Devil - Pretty much a similar romance plot to Strong Woman Do Bong Soon, except that 2ML had better reasons not to show his interest in FL in the initial part of the story. And ML unequivocally convinced 2ML that he was better for FL.