What is the difference between "may be not" and "may not be" ?
- She may be not a student.
- She may not be a student.
==> Do the two sentences have the same meaning?
 She may be not a student, ...
Meaning => True, she is not a student, she's a teacher, but she works just as hard as a student. She studies English at home on her own time.
 She may not be a student.
Meaning => There is a possibility that she is not a student.
Modal may, like modal must, is ambiguous between epistemic and deontic modality:
Ex: She may go to school.
=> permission; e.g., she is allowed to go.
Ex: She may not go to school.
=> permission to go to school is denied.
Ex: She may be at school.
=> possibility;e.g., It is possible that she is at school.
Ex: She may not be at school.
=> There's a possibility that she is not at school.
Ex: She may be not at school, but ...
=> True, she is not at school, she's at home, but she's at home studying right now as if she were in school.
Does that help?