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If I am understanding correctly, you would like to create a form so your students can register to different classes. If I am wrong, please feel free to correct me.
This is possible by using the Appointment Slot Widget.
Instead of having days, you may enter the different classes you offer to the student and the max number each class can have.
I have created a small form in which a student enters his name and has the option to register to 4 classes (math, english, biology and chemistry)
You may clone and review the form if you like.
Please let us know if this helps.