Recent developments in Large Language Models (LLMs) have significantly expanded their applications across various domains. However, the effectiveness of LLMs is often constrained when operating individually in complex environments. This paper introduces a transformative approach by organizing LLMs into community-based structures, aimed at enhancing their collective intelligence and problem-solving capabilities. We investigate different organizational models-hierarchical, flat, dynamic, and federated-each presenting unique benefits and challenges for collaborative AI systems. Within these structured communities, LLMs are designed to specialize in distinct cognitive tasks, employ advanced interaction mechanisms such as direct communication, voting systems, and market-based approaches, and dynamically adjust their governance structures to meet changing demands. The implementation of such communities holds substantial promise for improve problem-solving capabilities in AI, prompting an in-depth examination of their ethical considerations, management strategies, and scalability potential. This position paper seeks to lay the groundwork for future research, advocating a paradigm shift from isolated to synergistic operational frameworks in AI research and application.