Hermione takes twelve classes with a time-turner, and she drops two to get ten O.W.L.'s. You can even take more because Percy (and others) ended up with twelve O.W.L.'s. possibly without a time-turner.
Is twelve the most classes a Hogwarts student can take in their O.W.L. years?
I say that the maximum is twelve (12) because of the O.W.L. restriction placed on the question.
The courses offered at Hogwarts are as follows.
First Year Compulsory Classes:
Third Year Electives (minimum 2):
Offered based on demand in Sixth and Seventh Years:
Since O.W.L.s are given in the fifth year of education, I do not think the exam would be given for Alchemy (or at least there is not information to determine this).
There is no clear answer to how many classes the school offers total, 12 seems to be the max owls anyone gets.
So how many classes you can take without needing a time tuner, would depend entirely on the current teachers class schedules.
Hermione needed a time tuner due to her classes being scheduled in the same block, but during other years those classes may have all been staggered enough for someone like Bill or Crouch Jr. to take 12 classes without a Time Tuner.
I’ve been turning it back so I could do hours over again, that’s how I’ve been doing several lessons at once, see? - Prisoner of Azkaban
On top of that Bill and Crouch Jr. could have had Time-Tuners anyway, but since their forbidden to tell anyone about it we wouldn't know.
