You are not quantifying volume properly.
If you are saying that you need to train 10-15 sets per muscle group and that you can't do it in one session you are correct. You break up the muscle groups and do something like train chest on monday for 10-15 sets. then, you waite to train chest again until next week. So, in actuality, you have trained 10-15 sets on chest in one week (7 day rotation).
Now, if I train bench press for 4 sets on monday, DB incline press for 4 sets on wed. and incline BB press for 4 sets on fri., have I not done the exact same total amount of volume that you have done in a weeks time?
The only difference is that metabolic recovery will take place in around 48 hours. Why not give myself that additional training stimulus instead of waiting a week (a full 7 days) to do it again?