We present a novel method to hierarchically cluster networked data allowing nodes to simultaneously belong to multiple clusters. Given a network, our method outputs a cut metric on the underlying node set, which can be related to data coverings at different resolutions. The cut metric is obtained by averaging a set of ultrametrics, which are themselves the output of (non-overlapping) hierarchically clustering noisy versions of the original network of interest. The resulting algorithm is illustrated in synthetic networks and is used to classify handwritten digits from the MNIST database.