Overlay one multi-page PDF over another multi-page PDF

I need to overlay two multi-page PDFs - one containing the main content, the second containing a unique label at the bottom of each page - to produce a single PDF where each page shows its own corresponding label.

The Background and Watermark tools get me closest (Tools → Edit PDF → Background / Watermark).

Both accept a multi-page PDF as the label source, but then only allow a single numeric page number to be selected from it, so the same label appears on every page. If there were a "use all pages" or page-range option at that point, this would be straightforward.

Is there a way to achieve a true page-by-page overlay in Acrobat Pro?

Thanks.