We present a multi-agent reflective architecture for event extraction based on generativelarge language models (LLMs). Our architecture is the first of its kind to perform Semi-Open Event Extraction (SOEE), a hybrid framework that combines a fixed set of event template fields with dynamically generated attributes. Another novel feature of this system is the self-reflection. This type of LLM-based reasoning is the other novel feature of our system. It is defined as the generation of questions about missing or implicit event information and finding their answers within the system itself. We model event extraction as an iterative dialogue between a reflective LLM based agent, which generates questions to uncover missing event information and a set ofexpert agents, which provide domain-aware answers to these questions. The expert agents alsogenerate the initial event template using a generative LLM. Evaluated in the health domain, our event extraction system shows very promising results, demonstrating that LLM-based reflective multi-agent reasoning can accurately perform event extraction and expand the eventtemplate in a creative and comprehensive manner