Without any more information, the general response is yes you can start a business.
A couple of things to keep in mind:
- You may have limitations on the involvement in said business until your application is complete
- If you are sponsored by an employer you will have to continue working for them full time.
You should discuss the specifics of your situation with an immigration attorney.is happy to put you in touch with a qualified immigration attorney that can provided customized support throughout the entire green card process. Get in touch if you’d like a consultation.