Yes you can.
Only immigration consideration that comes to mind is that you must continue to work for your GC sponsor. You cannot get a green card through a business that you, or a relative, own more than 5% of.
Your tax considerations would be no different than anybody else running a business. I'd recommend that you contact a business lawyer and/or accountant for advice on what type of company to form. The only type that you cannot create is an S-Corp. (due to your immigration status)
Hope that helps
Regards and best of luck in your endeavor.
Rav