I posted this question in this section because the webpage containing this feature is generated by a JSP page.
I'm going to move this to the HTML forum because the fact that a JSP was used to generate the page is moot. Once it gets to the browser, it's an HTML page like any other, and there is no JSP mechansim that is applicable to this issue.
You basically are either going to have to use an applet or add multiple file upload fields. Problem with the file upload field is it contains strict security since an evil person could grab files that you would not want to be uploaded.