The first question I would ask is what are the requirements you are trying to implement? In all likelihood trying to use /apps/dam/Asset/GET.jsp is the wrong approach.
If you look at the recent request console in Felix (http://localhost:4502/system/console/requests) after you viewed a PDF in instance without your custom /dam/Asset/GET.jsp you will see that the code rendering the PDF is actually a chain of servlets - first com.day.cq.dam.core.impl.servlet.BinaryProviderServlet, then com.day.cq.dam.core.impl.servlet.SafeBinaryGetServlet, and final the default get servlet org.apache.sling.servlets.get.DefaultGetServlet.
The simplest way to get control of the rendering of the PDF without adversely impacting other functionality is be to create /apps/dam/Asset/myselector.jsp instead of GET.jsp, and then when you reference the PDF in your component print out link as /content/dam/geometrixx/documents/GeoCube_Datasheet.pdf.myselector.pdf for example. That requires that you be printing the link out in a component you control however.
Now if you can't control the URL then another way to do it would be to create /apps/dam/Asset/pdf.jsp and put your logic there. That would result in all the DAM PDFs getting your logic. However if the logic is specific to a single component or subset of PDFs then that probably isn't the right way to do it.
If you only want a subset of your PDFs to get this special treatment than the best way would be to write a custom component that extends foundation Download component. Then you can control the URL and add a selector. You can also put the script that is rendering the PDF in with the custom component - /apps/myapp/components/customdownload/myselector.jsp. Then you can use a URL format that looks like the image URLs - /content/geometrixx/en/company/_jcr_content/par/3_1219086936652.img.jpg/1289480092880.jpg but instead something like /content/geometrixx/en/company/_jcr_content/par/3_1219086936652.myselector.pdf/1289480092880.pdf.