Existing machine learning (ML) modeling tools center around a single-user experience, where a single user collects only their own data to build a model. However, individual modeling experiences limit the valuable opportunities for clashing alternative ideas and approaches that can occur when learners work together; therefore, it often avoids encountering important issues in LM around data representation and diversity, which can emerge when different perspectives are represented in a group-constructed data set. To address this problem, we created Co-ML, a tablet-based application that allows learners to collaboratively build ML image classifiers through an end-to-end, iterative model-building process. In this paper, we demonstrate the feasibility and potential richness of collaborative modeling by presenting an in-depth case study of a family (two children aged 11 and 14 working with their parents) using Co-ML in a facilitated introductory ML activity. at home. We share the design of the Co-ML system and discuss how the use of Co-ML in collaborative activities has enabled beginners to collectively engage with data design considerations that have been underrepresented in previous work, such as data diversity, class imbalance and data quality. We discuss how a distributed collaborative process, in which individuals can take on different model building responsibilities, provides a rich context for children and adults to learn ML data design.