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This situation is not contemplated by the regulations. A best practice would likely be to solicit a new self identification, or give the opportunity to update the self-identification form for new applications. At least those that are not close in time to a previous one submitted by an applicant as information could change.
You can use this OFCCP audit checklist to ensure you're doing what is required to maintain OFCCP's regulations including VEVRAA, Section 503, and EO 11246. Or request a demo to streamline your compliance and recruiting efforts.