Our DD9 is something of an activity butterfly. She doesn't wholeheartedly commit to anything, but she always has different things going on. Currently it's down to gymnastics and Girl Scouts, but she was in a couple of plays over the last three months. She's taking a break from theater and plans to drop Girl Scouts soon. She has expressed an interest in beginning piano lessons (she had previously taken guitar) and has decided to jump back into soccer this year, after having taken the previous year off.
Our DD was 6 when she started pushing to have more activities, just like your DS is doing now. We warned her that it might be too much, but we did enroll her in enough things that she had one activity a day for at least an hour 6 days a week. It was very easy to let her have that experience, let her learn from it, and then work with her in transitioning to a lighter schedule. Armed with this experience, she largely self-regulates (as you can see above in her method of dropping things before adding), and we let her lead in this within our boundaries of respecting time conflicts, higher priorities, and price limits.
