Duplicate a shape em several pages

Copy-paste the shape in a new blank PDF page and Save as.

Then use the Watermark tool to import it in all pages, in this sample the shape is the yellow rectangle:

Can you show us a screen shot of what you are trying to do?

This sounds like something that would best be done on the original file and then export to a new pdf.

Are you comfortable with InDesign? If so, you can use the "place multipage PDF" script to create a new InDesign file from your pdf, then add any additional content to the parent page and export to a new pdf, or apply the parent page to only those pages that need the extra content.

There are several ways of doing it. You can save the shape as an image file, apply it as the icon of an image field, and then duplicate that field to all pages. Or you can add it using the Square commenting tool and then use a script to duplicate it from the page you added it to all other pages.