Understanding social interactions involving both verbal and non-verbal cues is essential for effectively interpreting social situations. However, most prior works on multimodal social cues focus predominantly on single-person behaviors or rely on holistic visual representations that are not aligned to utterances in multi-party environments. Consequently, they are limited in modeling the intricate dynamics of multi-party interactions. In this paper, we introduce three new challenging tasks to model the fine-grained dynamics between multiple people: speaking target identification, pronoun coreference resolution, and mentioned player prediction. We contribute extensive data annotations to curate these new challenges in social deduction game settings. Furthermore, we propose a novel multimodal baseline that leverages densely aligned language-visual representations by synchronizing visual features with their corresponding utterances. This facilitates concurrently capturing verbal and non-verbal cues pertinent to social reasoning. Experiments demonstrate the effectiveness of the proposed approach with densely aligned multimodal representations in modeling fine-grained social interactions. Project website: https://sangmin-git.github.io/projects/MMSI.