I am not a fitness expert, but have long time experience fitting in "everything". I start my day always with morning run OR with the wonderful WAP video:-) Then I have weight training (3x/week) or swimming (4x/week). Every evening I have some core exercise (yoga, pilate or exercise ball). I have not seen any damage, though I am not in my 20s. (I am 46.)
I do not do anything because I have to do, I do because I enjoy all these. This is not a strict schedule, I travel a lot, it means frequent easy/rest days.
As I mentioned I am not an expert, but I am sure, if you listen to your body, you can do/fit many things.
Take care, and congratulation for your program:-))