In recent years various proposals have been offered for increasing the richness of the relational data model by addressing specific user requirements, particularly with regard to structural and behavioral expressiveness. Although there have been some criticisms of the semantic limitations of the model, few proposals have emerged to address them. In this paper we propose an extension of the model to address some of the semantic limitations around the use of multi-face attributes in everyday activity. We present a formal discussion of multi-face attributes and suggest how they can be accommodated in the relational model and relational database software systems. The resulting model offers a higher-level expressiveness and will provide the user with increased flexibility in the input, output and storage of data, and the specification of queries. Finally we outline some of the implications for database design methods that emerge for the extension.