The Calorimetric Electron Telescope (CALET) is a deep electromagnetic calorimeter designed for the measurement of cosmic-ray electrons on the International Space Station. Deployed on the Exposed Facility of the Japanese Experiment Module since August 2015, it observes cosmic-ray electrons with energies up to above 10 TeV and hadrons up to PeV total energies. Above a few TeV, the decrease in the electron flux and increased contamination by protons in the boosted decision tree (BDT) selection introduce challenges to determination of the flux at the highest energies and the search for signatures of nearby accelerators. To address the proton contamination, we apply a dedicated event-by-event analysis to evaluate the likelihood of each candidate event being a real electron or a contaminating proton. In this work, we detail the implementation of the likelihood analysis based on physically motivated shower parameters in the CALET calorimeter. Large simulated electron and proton datasets tailored to the parameters of the observed candidate events are generated and studied to produce a likelihood parameter for the improved rejection of protons. The results are tied to the BDT selection in the flight data analysis and summarized for the currently identified candidate events. Finally, we discuss an expansion of this work presently under development to use BDTs trained specifically for each candidate to provide an additional figure of merit.