I say do what you want, if you are able then by all means let her do what you'll allow.
I speak from experience. We have our 2nd grader in stuff all the time, nearly every night of the week she has something. We have had the tap/ballet class for several years once a week, she also does gymnastics and tumbling at the same business.
Her schedule there last school year was:
M- off
T-Dance class tap/ballet, it was a recital year, she was in 2 numbers, so there were a lot of extra practices throughout the Spring.
W-Tumbling at 4 and gymnastics at 5.
Th, F, and Sat no formal plans.
She does BMX on the weekends on Sunday for about 2 hours and does pretty well. She has one 1st place trophy, lots of 2nd place ones, and a few 3rd place one. She enjoys it so much. We don't travel all over doing point races and Grands due to the cost and just not having good transportation. Once the 4 yr. old starts riding we may add in the traveling but that is the future and who knows.
This school year she wanted to add Hip Hop class. Plus she made the show team that goes places and represents the gym. She is excited about that so much, she is one of these kids that go down each isle at Walmart turning flips over and over and over. We have to carry hand sanitizer all the time.
This schedule is:
M-show team practice for 1 hour
T-Hip Hop 1 hour
W-tap/ballet for 1 hour
TH-show team practice 1 hour, tumbling 1 hour. We are keeping her inthe extra tumbling for a couple of months so she can work on her skills and keep them improving.
Still nothing on F or Sa.
Then add in BMX on Sundays. So, do we have you beat yet??? LOL.
My hubby does stuff with the 4 yr. old like going to the Y for swimming, T-Ball, Soccer clinic at the Y, etc...he has sensory issues and doesn't do well in activities where he has to wait his turn or stay in line, he does really well with things one on one.