The process for making a new search on the results page is slightly custom so the exact code needed will differ based on the implementation. Here is some general steps though.
You can start by adding in a new form on the results page. In this form you will create hidden form elements to hold the values that were submitted from the original search form. You would then add in your select list to this form. If you use the same submit button as the original search form then you will not need to alter the trigger of the currently applied search.
Once the form is on the page you will want to modify your DataAssist Search server behavior to make use of the new select list you have on the page. If you set it up like this the new search form should work just like your original search form but it will include the select list also. If you have all of the form elements from your original search form in place with their values set to the posted values from the first search form then the search will work the same but with the new values.
Please post back with any questions that you have about any of these steps and I will be glad to help you out with whatever I can.
