In traditional multi-instance (MI) learning, a single positive instance in a bag produces a positive class label. Hence, the learner knows how the bags class label depends on the labels of the instances in the bag and can explicitly use this information to solve the learning task. In this paper we investigate a generalized view of the MI problem where this simple assumption no longer holds. We assume that an interaction between instances in a bag determines the class label. Our two-level learning method for this type of problem transforms an MI bag into a single meta-instance that can be learned by a standard propositional method. The meta-instance indicates which regions in the instance space are covered by instances of the bag. Results on both artificial and real-world data show that this two-level classification approach is well suited for generalized MI problems.