Music genres allow to categorize musical items that share common characteristics. Although these categories are not mutually exclusive, most related research is traditionally focused on classifying tracks into a single class. Furthermore, these categories (e.g., Pop, Rock) tend to be too broad for certain applications. In this work we aim to expand this task by categorizing musical items into multiple and fine-grained labels, using three different data modalities: audio, text, and images. To this end we present MuMu, a new dataset of more than 31k albums classified into 250 genre classes. For every album we have collected the cover image, text reviews, and audio tracks. Additionally, we propose an approach for multi-label genre classification based on the combination of feature embeddings learned with state-of-the-art deep learning methodologies. Experiments show major differences between modalities, which not only introduce new baselines for multi-label genre classification, but also suggest that combining them yields improved results.