Existing beginner-friendly machine learning (ML) modeling tools focus on a single user experience, where a single user collects only their own data to build a model. However, solo modeling experiences limit the valuable opportunities for finding alternative ideas and approaches that can emerge when students work together; consequently, it often fails to find critical issues in ML around data representation and diversity that can arise when different perspectives are manifested in a group-constructed data set. To address this issue, we created Co-ML, a tablet-based app for students to collaboratively create ML image classifiers through an end-to-end iterative modeling process. In this paper, we illustrate the feasibility and potential richness of collaborative modeling by presenting an in-depth case study of a family (two boys ages 11 and 14 working with their parents) using Co-ML in a self-facilitated introductory activity. ML. at home. We shared Co-ML system design and contributed a discussion of how using Co-ML in a collaborative activity allowed learners to collectively engage in data set design considerations 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 how to design ML data sets.