Adding a row to a PDF form would require that you use a Dynamic XFA form and use LiveCycle designer to create the form. However, the Adobe Acrobat on mobile doesn't support Dynamic XFA. You won't be able to fill out the PDF on an iPad.
You can add a row of fields in an Acrobat form, but you can't "re-flow" the page, so there will have to be white space available for the fields before you created it. Or you could spawn an entire page full of fields. But those things are not going to work on an iPad.
Your best chance is to create these fields in advance, hide them and then display them when they are required. That might work on an iPad, especially if you use Readdle's PDF Expert.