You can register the new company, but you cannot engage in gainful employment while you are in the United States in a B-1/B-2 visa. You need to change your status to something that allows you to work, and you should consult with an immigration lawyer regarding what are your best options.
Run it? No
Change status & then run it? Perhaps, meet with an attorney ... I see some problems with a car dealership. But, they shouldn't be insurmountable with a good attorney helping you.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.
You cannot run the dealerhip since it would constitute working the United States and you do not have work authorization. You owe it to yourself to contact an immigration lawyer, whether myself or one of my colleagues. If you appreciate the time spent preparing this answer, kindly consider marking it BEST ANSWER or HELPFUL. Also, please be sure to read my disclaimer below. Good luck to you.
Dean P. Murray
The Murray Law Firm
560 Sylvan Avenue
Englewood Cliffs, NJ 07632
Mr. Murray's response is NOT legal advice and does NOT create an attorney-client relationship. You should NOT rely on this response. Mr. Murray's response was generated without conducting a full inquiry as would occur during a face to face attorney-client consultation. It is likely that the response above may be made less accurate, or become entirely inaccurate, as you, i.e. the questioner, disclose additional facts that should only be discussed during a private consultation with an attorney. I strongly recommend that you consult an attorney who is licensed to practice law in your state (or, in the case of immigration law, and attorney in ANY state), whereupon all relevant facts will be discussed. All responses posted by Mr. Murray on Avvo.com are intended as general information for the education of the public, and not for any specific individual.
Anyone can form and own a business in the United States. Working in that business requires appropriate authorization. Whether a change of status would be viable in your case depends upon its specific facts. Consult with an experienced immigration attorney for case specific advice.
While this answer is provided by a Florida Bar Certified Expert in Immigration and Nationality Law, it is for general information purposes only and an attorney/client relationship is neither intended nor created. You should seek out qualified counsel to review your case and provide you with advice specific to your situation. Call +1-561-478-5353 to schedule a consultation with Mr. Devore.