Stance detection in social media is a well-studied task in a variety of domains. Nevertheless, previous work has mostly focused on multiclass versions of the problem, where the labels are mutually exclusive, and typically positive, negative or neutral. In this paper, we address versions of the task in which an utterance can have multiple labels, thus corresponding to multilabel classification. We propose a method that explicitly incorporates label dependencies in the training objective and compare it against a variety of baselines, as well as a reduction of multilabel to multiclass learning. In experiments with three datasets, we find that our proposed method improves upon all baselines on two out of three datasets. We also show that the reduction of multilabel to multiclass classification can be very competitive, especially in cases where the output consists of a small number of labels and one can enumerate over all label combinations.