Federated learning (FL) is an emerging machine learning (ML) paradigm that enables heterogeneous edge devices to collaboratively train ML models without revealing their raw data to a logically centralized server. However, beyond the heterogeneous device capacity, FL participants often exhibit differences in their data distributions, which are not independent and identically distributed (Non-IID). Many existing works present point solutions to address issues like slow convergence, low final accuracy, and bias in FL, all stemming from client heterogeneity. In this paper, we explore an additional layer of complexity to mitigate such heterogeneity by grouping clients with statistically similar data distributions (cohorts). We propose Auxo to gradually identify such cohorts in large-scale, low-availability, and resource-constrained FL populations. Auxo then adaptively determines how to train cohort-specific models in order to achieve better model performance and ensure resource efficiency. Our extensive evaluations show that, by identifying cohorts with smaller heterogeneity and performing efficient cohort-based training, Auxo boosts various existing FL solutions in terms of final accuracy (2.1% - 8.2%), convergence time (up to 2.2x), and model bias (4.8% - 53.8%).