Supplementary EC proposes that, in addition to the intracranial cognition that has been studied in the past, there is also transcranial cognition that is "just like" intracranial cognition. (The qualifier "just like"covers a multitude of issues.)
Another way of thinking about this kind of EC is that it adopts a "fractal scaling" approach. In fractal scaling, one has structures at one size scale that are mirrored at a larger scale. So, think of Inga-Otto. Inga has memories on the size scale of the brain; Otto has memories on the size scale of brain-body-world.