Some recent work in supervised learning focuses on so-called multi-label domains where each example can belong to two or more classes at the same time. In particular, the situation raises issues with performance evaluation and computational costs. But in domains with great many classes, there is yet another problem: what if the classes are not mutually independent as is the case in certain geneprediction problems where the inter-class relations are specified by DAG graphs? The talk reports our recent experience with classifier induction in these kind of domains. The individual topics include performance criteria for hierarchical multi-label classification, threshold adjustment in SVM classifiers, training-set creation, and error propagation through the DAG graph.