This study explores the critical challenge of balancing energy supply, investment efficiency, and profitability during the transition of natural gas enterprises into "natural gas+ " integrated energy systems. In a dynamic and uncertain environment, these systems face competing objectives: the carbon neutrality, resource optimization, and financial sustainability. To address these complexities, this study proposes a System Dynamics-Multi- Objective Programming (SD-MOP) model, grounded in the "Business-Production-Investment-Financial-Target" (BPIFT) framework, to integrate production, investment, and financial planning. The model incorporates SD to capture dynamic feedback among production, investment, and financial processes; MOP to resolve conflicting goals; Monte Carlo simulations to assess uncertainties across 200 scenarios; and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to generate Pareto-optimal solutions. Results identify key variables, such as the Reserve Replacement Ratio (RRR) and Single Well Production (SWP), as critical for maintaining system stability. Scenario analyses demonstrate that the model balances competing objectives, achieving a 14% improvement in energy supply and a 19% increase in profitability, while highlighting the trade-offs between maximizing energy supply and profitability under manageable investment levels. Overall, these findings establish the model as a practical decision-making tool for integrated energy enterprises, aligning enterprise strategies with sustainability goals.