This paper proposes the iHOMER (Incremental Hierarchy of Multi-label Classifiers) framework to address the challenges of mining data streams with multi-label outputs, particularly those facing evolving distributions, high-dimensional label spaces, sparse label occurrences, complex label dependencies, and concept shifts. iHOMER is an online multi-label learning framework that incrementally partitions the label space into mutually exclusive and correlated clusters without a predefined hierarchy. It guides instance segmentation by leveraging Jaccard similarity-based online split-set clustering and a global tree-based learner driven by a multivariate Bernoulli process. It also integrates global and local movement detection mechanisms to address anomalies and enable dynamic label splitting and subtree reconstruction. Experimental results on 23 real-world datasets demonstrate that iHOMER outperforms existing state-of-the-art global and local methods by 23% and 32%, respectively.