Network functions virtualization (NFV) enables telecommunications service providers to realize various network services by flexibly combining multiple virtual network functions (VNFs). To provide such services, an NFV control method should optimally allocate such VNFs into physical networks and servers by taking account of the combination(s) of objective functions and constraints for each metric defined for each VNF type, e.g., VNF placements and routes between the VNFs. The NFV control method should also be extendable for adding new metrics or changing the combination of metrics. One approach for NFV control to optimize allocations is to construct an algorithm that simultaneously solves the combined optimization problem. However, this approach is not extendable because the problem needs to be reformulated every time a new metric is added or a combination of metrics is changed. Another approach involves using an extendable network-control architecture that coordinates multiple control algorithms specified for individual metrics. However, to the best of our knowledge, no method has been developed that can optimize allocations through this kind of coordination. In this paper, we propose an extendable NFV-integrated control method by coordinating multiple control algorithms. We also propose an efficient coordination algorithm based on reinforcement learning. Finally, we evaluate the effectiveness of the proposed method through simulations.