Conversations involving three or more agents often occur in multi-agent systems, for example in brokering and auction protocols typically used in e-commerce. For developing agents in open systems, it is important that the interactions in such conversations have a precise and unambiguous meaning. We address this issue by generalising a protocolbased semantic framework for expressing the semantics of Agent Communication Languages. The generalisations involve exploiting mechanistic aspects of the interaction (conversation identifiers), greater flexibility in the space of possible replies, and a richer representation of protocol states. We define intentional specifications for some brokerage and auction protocols, including event-based clocks to determine the ordering of events. We then discuss how these agent interaction protocols can be integrated with internet protocols, using the Agent Communication Transfer Protocol (ACTP), an application layer protocol designed to generalize comm...