I'm not sure if it's possible. I worked at Sears a few years ago, and we used their SSN and Driver's License to apply on the computer. Right away, it would approve or deny the application. I didn't know about ITIN then, but I know I tried applying for customers before, and it didn't work. I figure they were using a fake SSN, but I don't know.
I had a guy walk (more like run) out on me during an application after I told him that I was going to put in the SSN and DL he gave me. I think his documents were fake.

I guess you can try with your ITIN and a valid ID. I never have.