Immigration Law Questions? Ask an Immigration Lawyer.
Please be aware that I cannot provide specific legal advice in this forum, because no lawyer client relation exists. Rather, I can only speak generally to aspects of the law and hypotheticals.
The short answer is "yes."
Generally, visas/immigration status and business ownership in the U.S. are independent of each other.
I know of no express USCIS regulation prohibiting foreign nationals from starting or owning a business.
Now, if you wanted to use the business as the means to obtain a nonimmigrant visa under the E category of "treaty investor" then your business plan/purchase would have to meet certain criteria in terms of amount and prospective employment in order to qualify. Generally, that's around $100,000 with a feasible business plan to sustain an ongoing business that employs several people.