It's not so clear from your question what you want to do. Search Generic is a text input field, not a dropdown.
You can add multiple fields to your search, and if the fields are not already dropdown (eg: SELECT->SIMPLE) then you can often make dropdowns with the SELECT-DYNAMIC field, where depending on the type of dropdown, you may need to use an SQL Query to pull data in from your database.
Eg:
I have a text field with storage field - year
I make another select dynamic field with the same storage field - year