This paper proposes a novel algorithm that resolves the underlying ambiguity in shape correspondences between symmetric objects. Due to the equivocal nature of symmetry, each part of a symmetric object may have two or more correspondence candidates in another symmetric object, which may induce local inconsistencies in the correspondence of parts or global ambiguities in shape matching. As an effective approach for resolving these symmetric ambiguities, we find multiple probable solutions for consistent shape correspondences between two 3D symmetric objects and let the user select one of them for an application-specific purpose. We formulate the problem of 3D symmetric object correspondences with a Markov Random Field (MRF) and iteratively search multiple solutions by excluding previously found solutions using Linear Programming (LP). The consistency of each solution is provided by four-point correspondences as high-order measurements in our MRF network, with each node corresponding to a point pair and each edge corresponding to a pair of point pairs. By leveraging the properties of the symmetry structure of the 3D object, we further reduce the complexity of our MRF network while efficiently handling high-order measurements. Finally, we evaluate the proposed algorithm using real-world symmetric object datasets.