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Multivariate singular spectrum analysis (M-SSA), with a structured varimax rotation, is a method that allows a deep characterization of phase synchronization (PS) phenomena in an almost automatic fashion. It has been increasingly used in the study of PS in networks of nonlinear, real-world, and numeric systems. This paper investigates the impact of the other recently developed structured orthomax rotations on the M-SSA ability to characterize PS. The results show that by using the structured quartimax rotation, a very faint and intermittent PS regime can be detected, in contrast with the structured varimax (which demands a stronger, more consolidated PS regime). This is due to the fact that the different rotations do not have the same efficiency in achieving a simple structure of the M-SSA eigenvectors. Nevertheless, for well-established PS regimes, the same robustness of the original M-SSA approach against high levels of additive Gaussian noise was found for the structured quartimax and biquartimax rotations. However, for all approaches we found an overshoot of the qualitative range for the PS onset due to noise.