In exploratory visualization systems, interactions allow to manipulate a visual representation and thereby gain insight into its supporting data. The responsiveness of these interactions is crucial, but achieving it on common hardware becomes increasingly difficult with the ever-growing size of datasets. Moreover, the representation of a large dataset itself is challenging since screen space is limited and, past a certain size, the number of items exceeds the number of pixels available or may render the representation unhelpful. The focus of this paper is on multidimensional data and parallel coordinates. For the system to be scalable, we propose a multiscale representation based on hierarchical aggregation on the client-side and distributed computing on a horizontally scalable infrastructure on the server-side. Multiscale visualization builds on several levels of abstraction to provide interactive and incremental changes in the level of detail. Horizontal scalability refers to the ability to increase the resources of the computing infrastructure by connecting additional computers. This paper presents: (1) a graph-based formalism for describing multiscale representations of parallel coordinates and their interactions and (2) a client-server system with a focus+context representation for multiscale parallel coordinates and distributed computation on a remote data-intensive infrastructure. We leverage the proposed formalism to describe several design possibilities for usual interactions in parallel coordinates, hierarchical navigation, and edition. We illustrated the scalability and usage of the representation in a real-world case. Performance experiments demonstrate that on a 15-computer cluster, the prototype system can scale to billion-item datasets while preserving the interactivity for analysis.