In order to study real-world systems many works model them through signed graphs, i.e. graphs whose edges are labeled as either positive or negative. Such a graph is considered as structurally balanced when it can be partitioned into a number of modules, such that positive (negative) edges are located inside (in-between) the modules. When it is not the case, authors look for the closest partition to such balance, a problem called Correlation Clustering (CC). The standard approach used in the literature is to find a single partition and focus the rest of the analysis on it, as if it was sufficient to fully characterize the studied system. Yet, it may not reflect the structure of the network, and one may need to seek for other partitions to build a better picture.