ModelAdmin - Can you add sub tabs to a managed model view?

Question

Silverstripe 3

I have a ModelAdmin setup with four managed models. When you load the ModelAdmin by clicking in the left menu, you see each managed model separated at the very top tab row.

For one of these managed models, I want to have the sub tab row display a separate gridfield for a subset of the managed model data. Note I am not trying to add sub tabs to the model itself. I know that can be achieved using getCMSFields and addFieldsToTab.

Is there an equivalent of doing this on the managed model view before users click into an actual instance of the model?

EDIT: Alternative solution I just thought of - being able to add a new top level tab to a page along side "Content", "Dependant Pages" and "Settings".