Using Advanced Search functions within the MediaBeacon web interface will allow you to combine AND and OR operators. However, this functionality can be difficult to find.
In the Advanced Search menu, create a new Saved Search using either AND or OR as your criteria conjunction and add your fields.
Run the search and then reopen the Advanced Search Menu.
Click Search within current results checkbox in the lower left.
Change the Criteria conjunction to either AND or OR. This should be the opposite of the criteria conjunction option selected in Step 1.
Add your fields and search values.
Click the Search button in the lower right.
Your correctly nested search will now be displaying over your view widget. Create a final Saved Search using both the AND and OR operators by clicking the File Save button to the right of the currently active search.