Study of the untoward effects associated with the comorbidity of multiple diseases on brain morphology requires identifying differences across multiple diagnostic groupings. To identify such effects and differentiate between groups of patients and normal subjects, conventional methods often compare each patient group with healthy subjects using binary or multi-class classifiers. However, testing inferences across multiple diagnostic groupings of complex disorders commonly yield inconclusive or conflicting findings when the classifier is confined to modeling two cohorts at a time or considers class labels mutually-exclusive (as in multi-class classifiers). These shortcomings are potentially caused by the difficulties associated with modeling compounding factors of diseases with these approaches. Multi-label classifiers, on the other hand, can appropriately model disease comorbidity, as each subject can be assigned to two or more labels. In this paper, we propose a multi-label transductive (MLT) method based on low-rank matrix completion that is able not only to classify the data into multiple labels but also to identify patterns from MRI data unique to each cohort. To evaluate the method, we use a dataset containing individuals with Alcohol Use Disorder (AUD) and human immunodeficiency virus (HIV) infection (specifically 244 healthy controls, 227 AUD, 70 HIV, and 61 AUD+HIV). On this dataset, our proposed method is more accurate in correctly labeling subjects than common approaches. Furthermore, our method identifies patterns specific to each disease and AUD+HIV comorbidity that shows that the comorbidity is characterized by a compounding effect of AUD and HIV infection.