The social stance advocated by institutional frameworks and most multi-agent system methodologies has resulted in a wide spectrum of organizational and communicative abstractions which have found currency in several programming frameworks and software platforms. Still, these tools and frameworks are designed to support a limited range of interaction capabilities that constrain developers to a fixed set of particular, pre-defined abstractions. The main hypothesis motivating this paper is that the variety of multi-agent interaction mechanisms – both, organizational and communicative, share a common semantic core. In the realm of software architectures, the paper proposes a connector-based model of multi-agent interactions which attempts to identify the essential structure underlying multi-agent interactions. Furthermore, the paper also provides this model with a formal execution semantics which describes the dynamics of social interactions. The proposed model is intended as the abstract machine of an organizational programming language which allows programmers to accommodate an open set of interaction mechanisms.