Explanations for algorithmic decision systems can take different forms, they can target different types of users with different goals. One of the main challenges in this area is therefore to devise explanation methods that can accommodate this variety of situations. A first step to address this challenge is to allow explainees to express their needs in the most convenient way, depending on their level of expertise and motivation. In this paper, we present a solution to this problem based on a multi-layered approach allowing users to express their requests for explanations at different levels of abstraction. We illustrate the approach with the application of a proof-of-concept system called IBEX to two case studies.