The ISS-based Calorimetric Electron Telescope (CALET) is directly measuring the energy spectrum of electron+positron cosmic rays up to 20 TeV. Annihilation or decay of dark matter (DM) could produce signatures in the positron and electron cosmic-ray spectra, thus the parameter space of DM candidate models can be probed by studying these messengers. The TeV-region extension of the spectrum provided by CALET is especially important for heavy DM search, since the signature’s location in energy is closely correlated with the DM mass.The magnet spectrometer AMS-02 on the other hand provides an exclusive positron-only spectrum below the TeV range. The combined analysis of both data-sets allows for DM search with a sophisticated modeling of the astrophysical background, comprising pulsars as the primary positron source and supernova remnant (SNR) sources providing the majority of the electron flux, in addition to a secondary component. As a refinement over a phenomenological power-law parametrization of the background, overlapping individual point source spectra are used as background for deriving limits on DM annihilation and decay from the CALET all-electron and the AMS-02 positron-only data. The used SNR and pulsar samples combine known nearby sources dominating the spectrum at high energies with randomly generated ones throughout the galaxy. By analyzing a large number of samples with also randomized emission spectra parameters, the expected variability of the background is taken into account, improving the reliability of the obtained limits on DM annihilation cross-section and lifetime.