In the multi-label data stream classification, concept drift and class-imbalanced are significant issues. Handling sparse data streams is also a considerable issue in it. Although the multi-label self-adjusting memory punitive kNN algorithm (MLSAMPkNN) proposed by Roseberry et al. is a hopeful framework for multi-label data stream classification, it has some limitations. Its punitive model removes data too quickly. Additionally, its performance with sparse and class-imbalanced data streams is not sufficient. Although we improved the its punitive model, the other limitations are remained unsolved. This paper proposes an algorithm for a multi-label self-adjusting memory kNN classifier that addresses not only drifting data streams but also sparse and class-imbalanced data streams. We changed the distance system and voting system of MLSAMPkNN to handle sparse and class-imbalanced data streams. Our experimental results demonstrate that our proposed algorithms consistently outperform other comparative models involving drifting, sparse, and class-imbalanced data streams.