In this paper we propose and discuss a layered organization for a design space suitable for the visualization of and interaction with rich information environments, made of multimedia and multidimensional information, supporting multi-device deployment. We propose to associate each design space layer to a different category of information, corresponding to different user goals and exploration spaces. Extending the focus+context and overview+detail approaches typical of complex information visualization, the layered design space and the associated information categories cover a wide range from a global universe of discourse down into the ultimate data items, through discrete intermediate steps corresponding to refinements of details and of navigation functions. Each category defines an association with a specific knowledge goal, the deployment on a suitable class of devices and the access through adequate interaction techniques. Such design process is applied to two case studies, one in the domain of cultural heritage fruition, the other in energy consumption management.