As far as I know, you don't need to be a citizen or a permanent resident to become a member of an LLC (Limited Liability Company). Since LLCs are registered with your state, they won't stop you from doing it as long as you have a SSN and you pay Taxes (In case of an LLC, it will be reported in your individual 1040 as a passthrough income).About BCIS not letting you do that, I am not sure. DP.