Are they hiring you as an employee? For an I-9 they need two pieces of ID. It has been a while since I've administered those forms, but it seems the SSN would be required since the purpose of the form is to verify your eligibility to work in the U.S.
For a W-9, the tax form, you can use either your SSN or EIN. I have had to supply a copy of my DL and even current car insurance to a number of companies. There are also some that will require a photo.
Either way, be sure you have done your homework on the company before providing anything.
Equal rights for others does not mean fewer rights for you. It's not pie.
"I prefer someone who burns the flag and then wraps themselves up in the Constitution over someone who burns the Constitution and then wraps themselves up in the flag." -Molly Ivins
Never try to teach a pig to sing. It's a waste of your time and it really annoys the pig.