The issue at play is to facilitate the deployment of renewable energy sources by coordinating privately owned batteries to also support local power systems. Battery systems most often exclusively answer the individual objective of their owner (e.g., a reduction in the energy bill). This study intends to explore whether both paradigms, (i) minimizing individual costs and (ii) mitigating network constraints, are achievable for individual battery systems, and if not, what trade-offs are available. Most studies in the literature take a subjective stand in their valuation of individual costs versus grid constraints. A set of Pareto optimal solutions is explored to provide a full picture of the aforementioned trade-off. As such, a novel Multi-Objective Optimal Power Flow (MO-OPF) algorithm is developed to solve a convexified battery control problem. Results show the ability of the proposed methodology to provide a frame of reference to compare online battery controllers, e.g., if a controller can exploit synergies between individual and collective objectives or not. Further, and for the proposed scenario, local energy communities provide a strictly better set of Pareto optimal solutions than individually operated systems.