Your form is a form based on AcroForm technology. This means that the form is static. Every field in the form corresponds with a widget annotation for which an absolute position is defined on the page. You can not add any data on coordinates that are not predefined, hence you can not "add more rows". What you are asking for is impossible.
Take a look under the hood of your PDF:

There's an array of /Fields
and each field is defined by a dictionary that combines field entries and the entries of a single widget annotation. Each widget annotation has its fixed coordinates on the page.
It seems that you were looking for a dynamic form solution. In that case, you need a form based on the XML Forms Architecture (XFA). Your form is not an XFA form.
If you are in doubt about the difference between AcroForm and XFA technology, please download this free ebook: The Best iText Questions on StackOverflow. In this book you'll find the answer to several questions such as:
These and other answers will give you an idea of some alternative options.