Identity as a service.
Have things like "This person is authorized to work for U.S. Companies", "This person is certified in x."
Your company would check the verification and make sure it's valid but then delete the supporting documentation or anything identifying.
Never give any of the supporting documentation to the companies, just give them access to see basically checkmarks that show they fulfill x arbritrary requirements.
But only if the applicant actually applies to the job, to prevent metadata scraping.