Can I start a company if I am working for an organization already?

Just registering an LLC in his name should be fine.

He should check his employment agreement though and shouldn't compete with his employer or use his employer's resources do do anything for the LLC.

LLC's can have non-citizen owners unlike an S-Corp however I don't know if there are any extra legal steps due to being a non-citizen. As far as working for another company you want to make sure that you are not violating any agreement (e.g. non-compete). Also to be fully ethical you should be sure it will not hinder you to do your current job and you should think about talking to someone in legal or hiring about whether having your own business violates policies.

That said I work for another company and have started an LLC to do work on the side.

Aside from the legal issues, there are ethical issues, he should talk to his employer about it.

I would be annoyed if one of my employees started up a company while I was employing them, without telling me. I understand people's need to do this, if someone approached me and I wanted to keep them, I'd work out some arrangement to allow them time to focus on the project.

That said, the employer needs to create an atmosphere where employees feel they can approach their employer on such matters.

Yes, he can form a business entity (LLC, etc.) - he could do so even if he had a visa rather than a green card.

The benefit of the green card is that it allows him to work for the entity - something he could not do on many types of visas. Please see "Visa Basics for Foreign Entrepreneurs Coming to the U.S." at http://dana.sh/diDRaK.

Disclaimer: This information does not constitute legal advice and does not establish an attorney-client relationship.

Your friend needs individual legal advice.