As data collection grows more common in various domains, there is a call for adapted or newer methods of visualization to tackle magnitudes exceeding the number of available pixels on screens and challenging interactivity. Exploratory visualization of large data present two major challenges: perceptual scalability and processing scalability. The first is concerned with overcoming the fundamental limitation of screens and human perception. The second deals with efficiently processing large volumes of data to achieve responsive interactions. Multiscale visualizations are an effective technique for solving the first challenge that builds on several levels of data abstraction to provide the user with an initial overview and subsequent incremental detail. The focus of this paper is on multidimensional data, a ubiquitous form of data among large-scale data sets, and parallel coordinates, a representation largely used for this type of data. For this representation, defining abstractions and interactively generating levels is not straightforward. Building upon several previous aggregated parallel coordinates representations, we propose a unifying and thinking model for conceiving and describing multi-scale parallel coordinates and their interactions. Using this formalism, we present a focus+context representation which bounds the number of visual items with a fixed resolution parameter while supporting exploration up to the item-level. Processing scalability is addressed by carrying out computation in a distributed manner on a remote data-intensive infrastructure. Bounding the visual items ensures perceptual scalability but also bounds the data transfer between this infrastructure and the rendering client.