Taxonomy building is a task that requires interpreting and classifying data within a given frame of reference, which comes to play in many areas of application that deal with knowledge and information organization. In this paper, we explore how taxonomy building can be supported with systems that integrate machine learning (ML). However, relying only on black-boxed ML-based systems to automate taxonomy building would sideline the users' expertise. We propose an approach that allows the user to iteratively take into account multiple model's outputs as part of their sensemaking process. We implemented our approach in two real-world use cases. The work is positioned in the context of HCI research that investigates the design of ML-based systems with an emphasis on enabling human-AI collaboration.