At the moment dbFront only shows the two levels, Parent and Child as you observed. Adding a third layer would significantly increase the screen complexity and mess with the usability both for the user and as a developer. This especially becomes a problem on smaller screens.
My suggestion is to teach your users to open the child record as a main record if they want to drill down. There is a "Maximize" icon at the top right corner of each child record. They can right click on this to open it in a new tab.
If you still strongly want to see three levels then please send an email to [email protected] where we can continue the discussion further.