An Enterprise wide project structure can be created in many ways as shown in the attached image.
Although its not easy to stick to one type of structure whether its division-wise or location-wise, its a good idea to develop an EPS Plan for use within the tools such as P6 as part of Project Controls Procedures.
Most businesses go for hybrid structures and then wonder why do they have shared & overlapped responsibilities among individuals. The answer flows from the top, the EPS.
Good Luck !