In multi-stage processes, classical Data Envelopment Analysis (DEA) acts like a black box and measures the efficiency of decision-making units (DMUs) without considering the internal structure of the system. Unlike classical DEA, recent studies have shown that the overall system efficiency scores are more meaningful if researched using the Network DEA (NDEA) methodology. NDEA performs simultaneous efficiency evaluations of sub-processes and the entire system. Recently, the composition method integrated with multi-objective programming (MOP) has been preferred by many authors to alleviate the drawbacks of earlier methods such as decomposition, slack-based measure (SBM) and the system-centric approach. This study proposes a novel approach incorporating Multi-Choice Conic Goal Programming into the NDEA (MCCGP-NDEA). It provides a more accurate representation of the Pareto front by revealing potential Pareto optimal solutions which are overlooked by the composition methods. Due to its ability to modify stage weights based on the decision makers’ (DMs) preferences, it is likely to gather more samples from the Pareto surface. Computational results on available benchmark problems confirm that the proposed MCCGP-NDEA is a viable alternative to existing methods.