I had a look at the Acrobat SDK help files and got the information below.
What you describe can be achieved by using Templates, but I am not sure if it is possible if your users have only Acrobat Reader.
Due to security restrictions, the following script works only in the JavaScript console or as part of a Batch sequence. You won't be able to put it into a button.
//Put this into the Console or in a Batch command
//Create a template based on the first page of the PDF - edit the nPage number to suit your PDF
this.createTemplate({cName: "myTemplate", nPage: 0});
var myTemplateArray = this.templates;
var myTemplate = myTemplateArray[0];
myTemplate.spawn(this.numPages, false, false);
// Obtain the collection of templates:
var t = this.templates;
var T = t[0];
// Prevent file size inflation by using the XObject.
var XO = T.spawn(0, true, true);
for (var i = 1; i < 3; i++) //Duplicates the page twice - edit the number to suit your needs
T.spawn(i, true, true, XO);
The example above creates 2 additional pages based on the first page of the form. The field names on each page will be unique.
You can read more about templates at:
http://livedocs.adobe.com/acrobat_sdk/9.1/Acrobat9_1_HTMLHelp/JS_Dev_T emplates.80.2.html
I hope this helps.