How do I keep 'lower' bookmarks when splitting a pdf by 'top' bookmarks?

I don't know how the original document was created - we received it in pdf form.  I would guess it's a mix of formats  as there are scans, emails, possible word docs and excel charts in it.

There are 4 bookmarked sections (marked by "top bookmarks" - splitting the pdf by "top bookmarks" splits it at those points).  Within each of those sections, there are subsections (originally separate individual documents) marked by what I called "lesser" bookmarks.  I suppose "lower" bookmarks might have been more appropriate in relation to "top".  I've also seen "parent" and "child" bookmarks, though I'm not sure if those terms have other characteristics as well.  Like this, where ">" is a bookmark:

> SECTION 1

     > subsection 1 a

     > subsection 1 b

     > subsection 1 c

> SECTION 2

     > subsection 2 a

etc, etc

As far as expectations, I would like to be able to manage the printing the individual documents (the "subsections" or "lower" bookmarks) as individual files (via a batch print manager) instead of pieces of one big document.  I realize I could individually print them by manually going bookmark to bookmark, but as it is such a big pdf, I was hoping there was a less time consuming way to do it.  I had originally hoped that using the split function would split the pdf into the four main sections (it did) while keeping the "lower" bookmarks intact (it didn't) so I could then split those 4 new pdfs into their subsections as individual pdfs for subsequent printing via the batch program.