In the last few years, we have been able to see how terms like Mobile Edge Computing, Cloudlets, and Fog computing have arisen as concepts that reach a level of popularity to express computing towards network Edge. Shifting some processing tasks from the Cloud to the Edge brings challenges to the table that might have been non-considered before in next-generation Software-Defined Networking (SDN). Efficient routing mechanisms, Edge Computing, and SDN applications are challenging to deploy as controllers are expected to have different distributions. In particular, with the advances of SDN and the P4 language, there are new opportunities and challenges that next-generation SDN has for Fog computing. The development of new pipelines along with the progress regarding control-to-data plane programming protocols can also promote data and control plane function offloading. We propose a new mechanism of deploying SDN control planes both locally and remotely to attend different challenges. We encourage researchers to develop new ways to functionally deploying Fog and Cloud control planes that let cross-layer planes interact by deploying specific control and data plane applications. With our proposal, the control and data plane distribution can provide a lower response time for locally deployed applications (local control plane). Besides, it can still be beneficial for a centralized and remotely placed control plane, for applications such as path computation within the same network and between separated networks (remote control plane).