Possible to save in booklet order?

Hello,

In the print dialog box, you can have Acrobat (I'm using Pro DC) arrange pages for printing as a booklet. Rather than actually printing the PDF in booklet format, though, is it possible to just save the rearrangement as a PDF? (For example: 5.5" x 8.5" single pages are rearranged and merged into a new layout that consists of 11" x 8.5" 2-up pages.) Or is there some other place within Acrobat that allows you to collate and merge pages for booklet printing?

When I selected 'Save as PDF' once the booklet was set up in the print dialog, I got a message saying that saving as a PDF from the print menu is not supported. It must be done by going through Save As. But Save As doesn't offer booklet rearrangement.

Background: I added the cover pages to a PDF of single pages generated by someone else, and am handing off the complete PDF to another person to print. I would like the printing to be as easy as possible for that person (i.e., one file, double-sided, fold, done). I don't have access to the file used to generate the interior pages, so I can't re-export them in booklet order before adding my cover after the fact.