Multi-label data stream classification (MLSC) is a supervised machine learning problem where each instance in the data stream is classified into one or more pre-defined sets of labels. One of the domain difficulties of MLSC is concept drift. Furthermore, the class imbalance issue is still challenging and significant in MLSC issues. Roseberry et al. proposed the multi-label self-adjusting memory punitive k nearest neighbor algorithm (MLSAMPkNN). It is a hopeful candidate for a framework for MLSC that is robust to the concept drifts and the class imbalance issue. It is a multi-label kNN classifier with self-adjusting memory using a punitive model, and it deals with the concept drifts and the class imbalance issue. However, its punitive system only relies on the number of labels in the dataset using label-specific methodology. This is not good on some datasets with a small number of labels and takes a long time on large datasets. This paper proposes a multi-label kNN classifier with self-adjusting memory using a punitive model by improving the punitive model of MLSAMPkNN. It also shows its effectiveness through comparative studies between our proposed algorithm and MLSAMPkNN on the 30 benchmark multi-label datasets and drifting data streams with mixed concept drifts generated by three artificial concept drift generators of MOA.