Generally FI visa do not allow you to work in the US..
However, if it is totally passive income I believe you can and you will require an ITIN..
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Almost certainly, you can not but I recommend that you seek the counsel of a competent immigration attorney. There are several in Dearborn. Best of luck - Reese Serra
This advise is only being offered as a courtesy. We do not have an attorney-client relationship and I do not represent you.
Deriving income inside the U.S. as a "business owner" is "not passive." I believe that you cannot take action to become a business owner, while a student.
You can only derive income from investments and activities related to approved curricular or optional practical training. You should fall out of F-1status as a business owner, where the DHS learns of the situation.
Again, deriving income as a stockholder is arguably a different situation. If you engage in work, such as incorporate or seek a business license, then you are working. If you have concerns, then I recommend an appointment with a competent and experienced immigration attorney.
This is general information, not legal advice, and does not create an attorney client relationship.