The tagline must include the protected groups covered by OFCCP enforcement, but can include more. So if your staffing firm's tagline includes all the same protected groups in the client tag line, plus more protected groups, then the staffing firm's tagline will meet the OFCCP requirement. If the client name is mentioned in the advertisement, it is important that it be clear that both companies meet the obligation. (You need not post two tag lines, but make sure that the tag line is attributed to both companies.) Hope this helps.
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.