Spawning a copy of the Template requires using a script. This code will spawn a Template called "MyTemplate" as the last page of the file, with unique field names:
this.getTemplate("MyTemplate").spawn(this.numPages, true, false);
However, be aware that although the fields are uniquely named, they will have the same values as the original fields on the Template page, so it might be a good idea to clear them, but that will require a more complex script (or to hide the Template page so the fields in it are always empty).
Edited: Fixed small mistake in the code.
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