Hi Lucas,

Just to clarify, by 'advanced search box', do you mean the advanced search dialog? Or do you mean the search syntax block that allows users to directly type in Laserfiche search syntax?

Currently, there isn't a way to preform 'Or' type text-phrase searches in the Web Access quick search bar. The 'Text' search block in the advanced search dialog does provide a convenient UI for constructing these types of searches: 

If the customer is concerned users may struggle to find and configure the 'Text' search block, an administrator can configure the search block (add the block, set the drop down to 'Or'), save the search, and push saved search out to all users by copying the corresponding attribute to the everyone group. That way, users can simply open the dialog, load the saved search, and enter their specific terms.