MOSAIC is a multilingual, taxonomy-independent, and computationally efficient approach for radiology report classification. It is built on a compact, publicly available language model (MedGemma-4B) and supports both zero- and few-shot prompting and lightweight fine-tuning. MOSAIC has been evaluated on seven datasets in English, Spanish, French, and Danish, covering multiple imaging modes and labeling schemes. It achieves an average macro F1 score of 88 on five chest X-ray datasets, approaching or exceeding expert-level performance, requiring only 24 GB of GPU memory. Using data augmentation, it can achieve a weighted F1 score of 82 on Danish reports with only 80 annotated samples. The code and models are open source.