You can edit the grid in Evo at SU-A and add additional search options.  You can only select fields that are already defined as indexes in the file.

Before you go to SU-A to add additional lookups in a grid you must first get the name of grid which can be found at the bottom left of the look up screen in the search you are trying to edit.  I have added searches  to both field data and Sort keys, but prefer Sort Keys because the addition in sort keys allows my users to see the new choice in the normal search and keeps them from the extra step of going to the search screen tab.    
 
I found the above fairly easy but I cant figure out how to easily move a "search" "column header"  UP in Sort Keys. .  Maybe I am missing something?  
It is easy to change the display order in Field Data, but not so easy in Sort Keyes.  I wish I could insert the new choice where i want it in Search Key.    Here is what i am doing and i hope there is a better way in Search Keys.  1. add the new column header  to the bottom of Search Key. .   2.  retype and recreate several column headers  from the middle to the bottom.  3.  delete the middle column headers and now my new choice is in the middle and not the bottom.  I do this so that my users will not have to scroll the down the sort list when they are doing a search in look up screen in the opening list. a
Thanks,
Laura

To me it is awkward that to add a column in Field Data you simply choose the ADD button.  
But to add a column in Sort Keys you have to place your cursor in a used field and then use the arrow down button.  
 
It is awkward because it seems if Field Data has an ADD button them Sort Key should also have an add button.   Maybe there is a reason for this, but I don't understand.  I have to remind myself how to do this every time.
 
tag:  SU-A maintain drill downs