I am sorry, I wasn't clear enough in my post.
I have the multiple autocomplete fields working fine. The user can start typing and the autocomplete box is displayed, and the use can select a displayed option, or enter in their own.
What I would like to do, is add a drop down button (triangle) next to the field, so the user can click on it, and the auto-complete box would automatically activate and show all of the possible options.
To be even clearer, I am using the jquery-ui widget.