Centralized Multiport Networked Dynamic (CMND) systems have emerged as a key architecture with applications in several complex network systems, such as multilateral telerobotics and multi-agent control. These systems consist of a hub node/subsystem connecting with multiple remote nodes/subsystems via a networked architecture. One challenge for this system is stability, which can be affected by non-ideal network artifacts. Conventional passivity-based approaches can stabilize the system under specialized applications like small-scale networked systems. However, those conventional passive stabilizers have several restrictions, such as distributing compensation across subsystems in a decentralized manner, limiting flexibility, and, at the same time, relying on the restrictive assumptions of node passivity. This paper synthesizes a centralized optimal passivity-based stabilization framework for CMND systems. It consists of a centralized passivity observer monitoring overall energy flow and an optimal passivity controller that distributes the just-needed dissipation among various nodes, guaranteeing strict passivity and, thus, L2 stability. The proposed data-driven model-free approach, i.e., Tunable Centralized Optimal Passivity Control (TCoPC), optimizes total performance based on the prescribed dissipation distribution strategy while ensuring stability. The controller can put high dissipation loads on some sub-networks while relaxing the dissipation on other nodes. Simulation results demonstrate the proposed frameworks performance in a complex task under different time-varying delay scenarios while relaxing the remote nodes minimum phase and passivity assumption, enhancing the scalability and generalizability.