Handling multi-party dialogues represents a significant step for advancing spoken dialogue systems, necessitating the development of tasks specific to multi-party interactions. To address this challenge, we are constructing a multi-modal multi-party dialogue corpus of triadic (three-participant) discussions. This paper focuses on the task of addressee recognition, identifying who is being addressed to take the next turn, a critical component unique to multi-party dialogue systems. A subset of the corpus was annotated with addressee information, revealing that explicit addressees are indicated in approximately 20% of conversational turns. To evaluate the task's complexity, we benchmarked the performance of a large language model (GPT-4o) on addressee recognition. The results showed that GPT-4o achieved an accuracy only marginally above chance, underscoring the challenges of addressee recognition in multi-party dialogue. These findings highlight the need for further research to enhance the capabilities of large language models in understanding and navigating the intricacies of multi-party conversational dynamics.