Within the field of argument mining, an important task consists in predicting the frame of an argument, that is, making explicit the aspects of a controversial discussion that the argument emphasizes and which narrative it constructs. Many approaches so far have adopted the framing classification proposed by Boydstun et al. , consisting of 15 categories that have been mainly designed to capture frames in media coverage of political articles. In addition to being quite coarse-grained, these categories are limited in terms of their coverage of the breadth of discussion topics that people debate. Other approaches have proposed to rely on issue-specific and subjective (argumentation) frames indicated by users via labels in debating portals. These labels are overly specific and do often not generalize across topics. We present an approach to bridge between coarse-grained and issue-specific inventories for classifying argumentation frames and propose a supervised approach to classifying frames of arguments at a variable level of granularity by clustering issue-specific, user-provided labels into frame clusters and predicting the frame cluster that an argument evokes. We demonstrate how the approach supports the prediction of frames for varying numbers of clusters. We combine the two tasks, frame prediction with respect to media frames categories as well as prediction of clusters of user-provided labels, in a multi-task setting, learning a classifier that performs the two tasks. As main result, we show that this multi-task setting improves the classification on the single tasks, the media frames classification by up to +9.9 % accuracy and the cluster prediction by up to +8 % accuracy.