Generating PDFs that include PDFs from Media/file fields

I'm working on using Entity Print to create PDFs from nodes where one content type contains a (Paragraph whose fields include a Media field, which has a) file field where content editors can add PDF files. Therefore, I'm trying to create a PDF that includes a PDF.

By default, Drupal uses the Generic file display format for file fields' display settings. That produces a link to the file, which I can see reproduced in the PDF. Ideally, I'd like the Entity Print-generated PDF to include the contents of the PDF field as well. Is there a way to do that? I tried to see if the PDF Reader → module would help, but while it prints the PDF for the regular node on the Drupal front end, it doesn't display anything in the generated PDF.

Sorry if there's already information somewhere about this—this was somewhat tough to search for. :)