The top-k classification accuracy is one of the core metrics in machine learning. Here, k is conventionally a positive integer, such as 1 or 5, leading to top-1 or top-5 training objectives. In this work, we relax this assumption and optimize the model for multiple k simultaneously instead of using a single k. Leveraging recent advances in differentiable sorting and ranking, we propose a family of differentiable top-k cross-entropy classification losses. This allows training while not only considering the top-1 prediction, but also, e.g., the top-2 and top-5 predictions. We evaluate the proposed losses for fine-tuning on state-of-the-art architectures, as well as for training from scratch. We find that relaxing k not only produces better top-5 accuracies, but also leads to top-1 accuracy improvements. When fine-tuning publicly available ImageNet models, we achieve a new state-of-the-art for these models.