If you're looking for manga similar to Fruits Basket, you might like these titles. All recommendations are made by Anime-Planet users like you!
Both manga are based around the 1 girl, 2 guys love triangle deal. The female leads are both cute and cheerful girls with a lot on their plate. They both have supernatural themes without being overly annoying about it (imo). If you liked one, I would say that you would almost definately enjoy the other.
Haine Otomiya is a student at the elite Imperial Academy. A one-time gang member who was put up for adoption by her father, her life changed when she met Shizumasa Togu, president of the student council and ‘emperor' of Imperial Academy. Haine quits her gang and enrolls at the prestigious private school in the hope of winning Shizumasa's love. When she is hired as his school bodyguard, she's thrilled; but can she survive the drama of the student council? As secrets spill and relationships form, Haine is pulled further into the world of the elite and powerful, where wealth is everything and social status is the basis of all relationships. What's a girl to do?
These two series are similar, in both setting and plot. The main character for both is a cheery highschool girl who ends up in a love triangle that only gets more and more complicated, expecially when the boys' powerful familes get involved. The high school setting and humor are also similar in both.Both series, although starting as simple romance stories, eventually dive into dark themes as well.