It doesn't work like that at all. You add GVA (https://en.wikipedia.org/wiki/Gross_value_added https://en.wikipedia.org/wiki/Gross_value_added) of each entities

It doesn't work like that at all. You add GVA (https://en.wikipedia.org/wiki/Gross_value_added https://en.wikipedia.org/wiki/Gross_value_added) of each entities. Adding more intermediate entities doesn't increase GDP as the GVA of each entities is reduced.