Conversational practices do not occur at a single unit of analysis. To understand the interplay between social positioning, information sharing, and rhetorical strategy in language, various granularities are necessary. In this work we present a machine learning model for multi-party chat which predicts conversation structure across differing units of analysis. First, we mark sentence-level behavior using an information sharing annotation scheme. By taking advantage of Integer Linear Programming and a sociolinguistic framework, we enforce structural relationships between sentence-level annotations and sequences of interaction. Then, we show that clustering these sequences can effectively disentangle the threads of conversation. This model is highly accurate, performing near human accuracy, and performs analysis on-line, opening the door to real-time analysis of the discourse of conversation.