Predicting Antimicrobial Resistance (AMR) from genomic data has important implications for human and animal healthcare, and especially given its potential for more rapid diagnostics and informed treatment choices. With the recent advances in sequencing technologies, applying machine learning techniques for AMR prediction have indicated promising results. Despite this, there are shortcomings in the literature concerning methodologies suitable for multi-drug AMR prediction and especially where samples with missing labels exist. To address this shortcoming, we introduce a Rectified Classifier Chain (RCC) method for predicting multi-drug resistance. This RCC method was tested using annotated features of genomics sequences and compared with similar multi-label classification methodologies. We found that applying the eXtreme Gradient Boosting (XGBoost) base model to our RCC model outperformed the second-best model, XGBoost based binary relevance model, by 3.3% in Hamming accuracy and 7.8% in F1-score. Additionally, we note that in the literature machine learning models applied to AMR prediction typically are unsuitable for identifying biomarkers informative of their decisions; in this study, we show that biomarkers contributing to AMR prediction can also be identified using the proposed RCC method. We expect this can facilitate genome annotation and pave the path towards identifying new biomarkers indicative of AMR.