The Calorimetric Electron Telescope (CALET) is a cosmic-ray observatory operating since October 2015 onboard the International Space Station (ISS). The data processed since the beginning of the mission has made it possible to measure with high precision the inclusive flux of cosmic electrons and positrons (all-electron) in the multi-TeV region. The appearance of any structures in this energy region can potentially be connected to the presence of nearby astrophysical sources or dark matter. The CALET detector, consisting of a charge detector, an imaging calorimeter and a total absorption calorimeter has a total vertical thickness of about 30 radiation lengths. The construction characteristics of the instrument allow to obtain an energy resolution better than 2% for electrons and a proton rejection power of about $10^5$. However, the exploration of the multi-TeV region involves dealing with a limited statistical sample and a large proton background. As a consequence, a complex multivariate analysis based on variables connected to the shower development has been adopted. In this contribution, we summarize the results of a study conducted on different multivariate analysis techniques in order to optimize the proton rejection at high energies in the all-electron flux measurement. In particular, we discuss the features of the different methods, the tuning of their parameters and the overall strategy to increase the separation between electrons and protons, avoiding the phenomenon of overfitting.