Compositional Zero-Shot Learning (CZSL) aims to learn semantic primitives (attributes and objects) from seen compositions and recognize unseen attribute-object compositions. Existing CZSL datasets focus on single attributes, neglecting the fact that objects naturally exhibit multiple interrelated attributes. Their narrow attribute scope and single attribute labeling introduce annotation biases, misleading the learning of attributes and causing inaccurate evaluation. To address these issues, we introduce the Multi-Attribute Composition (MAC) dataset, encompassing 22,838 images and 17,627 compositions with comprehensive and representative attribute annotations. MAC shows complex relationship between attributes and objects, with each attribute type linked to an average of 82.2 object types, and each object type associated with 31.4 attribute types. Based on MAC, we propose multi-attribute compositional zero-shot learning that requires deeper semantic understanding and advanced attribute associations, establishing a more realistic and challenging benchmark for CZSL. We also propose Multi-attribute Visual-Primitive Integrator (MVP-Integrator), a robust baseline for multi-attribute CZSL, which disentangles semantic primitives and performs effective visual-primitive association. Experimental results demonstrate that MVP-Integrator significantly outperforms existing CZSL methods on MAC with improved inference efficiency.