Abstract Multiscale entropy (MSE) is an appealing tool to characterize the complexity of time series over multiple temporal scales. Recent developments in the field have tried to extend the MSE technique in different ways. Building on these trends, we propose the so-called refined composite multivariate multiscale fuzzy entropy (RCmvMFE) whose coarse-graining step uses variance (RCmvMFE σ 2 ) or mean (RCmvMFE μ ). We investigate the behavior of these multivariate methods on multichannel white Gaussian and 1/ f noise signals, and two publicly available biomedical recordings. Our simulations demonstrate that RCmvMFE σ 2 and RCmvMFE μ lead to more stable results and are less sensitive to the signals’ length in comparison with the other existing multivariate multiscale entropy-based methods. The classification results also show that using both the variance and mean in the coarse-graining step offers complexity profiles with complementary information for biomedical signal analysis. We also made freely available all the Matlab codes used in this paper.