Customizing the "Customer Search" box

I have a customer request to be able to limit the customer search box to just Global Ultimate Accounts. They have multiple subsidiaries and children accounts with similar names. When searching into this box, the user could never pinpoint the specific ultimate within the massive amounts of results. 

They have a global ultimate field in SFDC so my thought would be to allow a filter on that box to just (for example) look at Global Ultimate != Null. This could allow for other customizations to this search.