If you talk to aurora during your free time, if you have enough transformations, she will unlock your body transformations faster. I have to admit though, i don't really know how does she decide if it's enough or not, i always get as much as i can, and only sometimes it works.
It's not the number of transformations that is the key point more how much you have transformed. Some transformations have a bigger effect (hair, eyes, nose and forehead) count for more than lips and jawline. I usually have hair and eyes maxed before talking to Aurora on the Saturday which is enough to unlock body transformation. This is covered in the walkthrough along with where and how to obtain the transformation points.