Significant progress has been made in the design and development of Grid middleware which, in its present form, is founded on Web services technologies. However, we argue that present-day Grid middleware is severely limited in supporting projected next-generation applications which will involve pervasive and heterogeneous networked infrastructures, and advanced services such as collaborative distributed visualization. In this paper we discuss a new Grid middleware framework that features (i) support for advanced network services based on the novel concept of pluggable overlay networks, (ii) an architectural framework for constructing bespoke Grid middleware platforms in terms of 'middleware domains' such as extensible interaction types and resource discovery. We believe that such features will become increasingly essential with the emergence of next-generation e-Science applications. Copyright (c) 2005 John Wiley & Sons, Ltd.