Feature modeling enables a straightforward representation of a product's features, components, and the relations between them. In this way, feature models serve as an excellent approach to diagrammatically model a product design for manufacturing purposes. However, the actual usage of such a feature model to generate suitable designs in the context of real-life industry applications is often limited, as crucial background knowledge cannot be expressed. Moreover, even though expert validation of a feature model is an important aspect of its creation, current tooling often falls short on this aspect. Indeed, although state-of-the-art tools are capable of generating possible configurations, this is not sufficient to completely validate complex applications: instead, we should enable the expert to interactively explore the problem domain. In this paper, we present our feature modeling tool, called FM-IDP, which aims to overcome both of these shortcomings. In FM-IDP, background knowledge can be expressed in FO(•), a rich extension of classical first-order logic. Using an off-the-shelf logical reasoning engine and an integrated interactive configuration interface, modelers can interact with the feature model and its background knowledge to explore the problem space on-the-fly. We motivate our approach using an industrial use case focused on real-life component design.