Editing Global Site Search Form

I'm trying to edit the Global Site Search form to allow the search to be filtered. Just to see what would happen, I added

<select name = "order">
<option value="ASC">asc</option>
<option value="DESC">desc</option>

But no matter what happened to the URL, the order of the posts did not change. When it comes to editing the search form and modifying this plugin's query to filter results what am I missing?