Fruits Basket Another, Vol. 1 by Natsuki Takaya-192 pages
Sawa Mitoma is starting at a new high school. She doesn't have very high self-confidence and tries not to be notices or cause any trouble. She is always looking down. However, when she is late for school on the first day, a handsome new classmate named Mutsuki, sticks up for her and over time he and his friends/family raise Sawa's self-confidence. Sawa learns that Mutsuki and his friends/family are Sohmas and Mutsuki and Hajime are Vice President and President on the student council. They invite her to be the first-year representative on the student council. Also, they invite her over for dinner after school on the 29th, which is meat day (because the Japanese word for meat and the word for 29 are similar). Over time, Sawa Mitoma gains confidence and feels like she is starting to fit in with the Sohmas.