I found the following javascript example for uploading multiple files in one session:
Upload multiple files with a single file element
My question is that in my APEX 3.2 page, I currently have a region that looks like this:

And I want to take out the default ‘File Browse’ and put in the multiple file upload portion in it’s place.

Is there a way to put a region within a region? If not, how can I add an HTML item within a region?
Here is the code that I have in the second screen shot (html region):
<form enctype="multipart/form-data" action="your_script_here.script" method = "post">
<input id="my_file_element" type="file" name="file_1" >
<input type="submit">
Files:
<div id="files_list"></div>
<script>
var multi_selector = new MultiSelector( document.getElementById( 'files_list' ), 3 );
multi_selector.addElement( document.getElementById( 'my_file_element' ) );
</script>
</form>
You can create a “Display as Text” item and set your HTML code as the source. Make sure that the item is not set to escape HTML, otherwise you will just see the HTML and not the controls.

The result comes out like this (I have a text item “Request Title” followed by the display item based on your HTML: