What you are proposing could be thought of as a search within a search so to speak.
You could have a page that has the results listed on it then have a select list to further filter the results. To make this work you would need to modify your DataAssist Search server behavior that is on the results page, you will want to add in another search criteria using the AND separator.
How you submit the info from the select list will determine how you specify the value for this new criteria, if you have the select list with a button next to it you could have the value submit from a form and use the posted value from the select list as the value in your new criteria.
So long as you do not trigger the Search Server behavior again it will use the last submitted search query along with this new value to further filter the results.
Please post back with any specific questions that you have about this and we will help with what we can.