What companies will approve you for credit using your tax identification number only?

I am guessing you mean approve you so you can receive credit from their business. The answer is no businesses. The business you have a Tax ID for is just an result of your own personal credit. They need to know everything about your own credit history to grant you credit. To do this they will need your credit references and/or your social security number to run a credit check and make sure your credit is A-Number One.