Velocity distribution functions (VDFs) measured by the Magnetospheric Multiscale (MMS) mission are complex 3D datasets that can be represented as a superposition of multiple beams (M. V. Goldman et al., 2020). A recent work (Dupuis et al., 2020) proposed the use of the Gaussian Mixture Model (GMM). Here we investigate the approach by considering first synthetic distributions made by artificially creating beams of either Maxwellian distributions or kappa distributions with varying power law index. By varying the inter-beam average difference and the beam standard deviation we evaluate the ability of the GMM in recognizing correctly the beam. We then apply the method systematically to MMS data in the tail and in the dayside. In this case, the data need preparation before being processed by the GMM to account for the specifics of the instrument and in particular the lack of data at low energy and to account for the noise in the counts. The conclusion of the analysis is that the GMM is capable of detecting the presence of multiple beams when their distinction is significant. The GMM can define reliably the complexity of a measured dataset in terms of the number of optimal beams provided by information theory criteria. Visual inspection confirms this automatic definition of complexity.