I haven't tried with Acrobat, but it is possible in LiveCycle/AEM form Designer. How to add button to insert duplicate page in form
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A template is an excellent option. Especially because they work in Reader XI and Reader DC!! It used to be that they only worked in Acrobat Pro and Standard.
You'll find a full template example file and tutorial in the downloads section of PDFScripting.com. Search for the word "Template".
But there are other ways to duplicate content. What is the purpose of duplicating the content? Does this involve form fields?