Building speech emotion recognition (SER) models that generalize across languages remains challenging due to limited annotations, linguistic diversity and heterogeneous label spaces. Current multilingual SER approaches either rely on fully shared models or restrict training to a small set of overlapping emotions that restrict diversity in expressiveness. We propose EMBRACE, a multilingual speech representation for language-agnostic SER. Drawing inspiration from partial-label learning paradigms in computer vision, EMBRACE adapts a unified superset emotion modeling strategy. The approach enables training on mixtures of datasets with non-overlapping emotion categories by selectively masking absent categories during optimization. To balance this complex multi-domain training, the model leverages a knowledge distillation based progressive training procedure that stabilizes multilingual optimization and mitigates catastrophic forgetting. Experiments across seven languages show that EMBRACE improves cross-corpus performance by 31.8% and in-corpus by 15.2% over strong emotional speech representations, confirming its ability to learn discriminative and transferable affective representations.