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The increasing complexity of Multi-Agent Systems (MASs), coupled with the emergence of Artificial Intelligence (AI) and Large Language Models (LLMs), have highlighted significant gaps in our understanding of the behavior and interactions of diverse entities within dynamic environments. Traditional game theory approaches have often been employed in this context, but their utility is limited by the static and homogenous nature of their models. With the transformative influence of AI and LLMs on business and society, a more dynamic and nuanced theoretical framework is necessary to guide the design and management of MASs. In response to this pressing need, we propose an Extended Coevolutionary (EC) Theory in this paper. This alternative framework incorporates key aspects of coevolutionary dynamics, adaptive learning, and LLM-based strategy recommendations to model and analyze the strategic interactions among heterogeneous agents in MASs. It goes beyond game theory by acknowledging and addressing the diverse interactions (economic transactions, social relationships, information exchange) and the variability in risk aversion, social preferences, and learning capabilities among entities. To validate the effectiveness of the EC framework, we developed a simulation environment that enabled us to explore the emergence of cooperation and defection patterns in MASs. The results demonstrated the potential of our framework to promote cooperative behavior and maintain robustness in the face of disruptions. The dynamics and evolution of the Multi-Agent System over time were also visualized using advanced techniques. Our findings underscore the potential of harnessing LLMs to facilitate cooperation, enhance social welfare, and promote resilient strategies in multi-agent environments. Moreover, the proposed EC framework offers valuable insights into the interplay between strategic decision making, adaptive learning, and LLM-informed guidance in complex, evolving systems. This research not only responds to the current challenges faced in modeling MASs, but also paves the way for future research in this rapidly developing field.