She is as rich as I (strictly grammatical).
She is as rich as me (common).
She is as rich as I am (the safest choice).
Student or Learner
- She is rich as well as I.
I would like to ask if we can use "as well as I" instead of "me"?
'She, as well as I, is rich.'
I think it is uncommon, yet it might be the OP's intended meaning, but I am not a teacher.
You can have: She and I are rich. or Both she and I are rich.
I am not a teacher.
I think 'She is rich, as am I' might also be the OP's intended meaning, but I am not a teacher.
I'm not a teacher and I'm not a native speaker of English.