An advanced decision support system (DSS) for implementing the Graph Model for Conflict Resolution (GMCR) is designed and illustrated using a real world conflict.The new system, called GMCR+, is capable of handling a wide variety of decision problems involving two or more decision-makers (DMs). Given the DMs, the options or courses of action available to each of them, and each DM's relative preferences over the possible scenarios or states that could occur, GMCR+ can calculate stability and equilibrium results according to a rich range of solution concepts that explain human behaviour under conflict. Then the inverse component of the DSS GMCR+ can determine what DMs' preference rankings of states must be in order to produce stable states and equilibria as specified by the user. Other features incorporated into GMCR+ include coalition analysis, graph and tree diagram visualisation, narrative reporting of results and a tracing feature that shows how the conflict could evolve from a status quo state to a desirable equilibrium or other specified outcome. The system GMCR+ has a modular design in order to facilitate the addition of further advancements.