Fact checking is an essential challenge when combating fake news. Identifying documents that agree or disagree with a particular statement (claim) is a core task in this process. In this context, stance detection aims at identifying the position (stance) of a document towards a claim. Most approaches address this task through a 4-class classification model where the class distribution is highly imbalanced. Therefore, they are particularly ineffective in detecting the minority classes (for instance, 'disagree'), even though such instances are crucial for tasks such as fact-checking by providing evidence for detecting false claims. In this paper, we exploit the hierarchical nature of stance classes, which allows us to propose a modular pipeline of cascading binary classifiers, enabling performance tuning on a per step and class basis. We implement our approach through a combination of neural and traditional classification models that highlight the misclassification costs of minority classes. Evaluation results demonstrate state-of-the-art performance of our approach and its ability to significantly improve the classification performance of the important 'disagree' class.