Due to the rapid advancements in recent years, medical image analysis is largely dominated by deep learning (DL). However, building powerful and robust DL models requires training with large multi-party datasets. While multiple stakeholders have provided publicly available datasets, the ways in which these data are labeled vary widely. For Instance, an institution might provide a dataset of chest radiographs containing labels denoting the presence of pneumonia, while another institution might have a focus on determining the presence of metastases in the lung. Training a single AI model utilizing all these data is not feasible with conventional federated learning (FL). This prompts us to propose an extension to the widespread FL process, namely flexible federated learning (FFL) for collaborative training on such data. Using 695,000 chest radiographs from five institutions from across the globe-each with differing labels-we demonstrate that having heterogeneously labeled datasets, FFL-based training leads to significant performance increase compared to conventional FL training, where only the uniformly annotated images are utilized. We believe that our proposed algorithm could accelerate the process of bringing collaborative training methods from research and simulation phase to the real-world applications in healthcare.