Beyond their differences, most black-box explanation methods share a number of features and can be framed in a common structure. We identify these features and propose a generic and parameterized framework which makes it possible to combine them in different ways. This framework has been implemented in a proof of concept system called IBEX (for “Interactive Black-box EXplanation system”). IBEX makes it possible to address a variety of needs of different types of explainees (e.g. local or global explanations, detailed or simple explanations, explanations in the form of counterfactuals, rules, plots, etc.). We illustrate the benefit of the approach in terms of versatility through several case studies corresponding to different types of explainees.