First-principles calculations using density functional theory and two methods in comparison, Quantum ESPRESSO and Siesta , are done on large supercells which describe different placements of two identical adsorbed alkali metal atoms (of either Na, or K species) on the monolayer of boron carbide BC3. The energy of single-atom adsorption over the center of C6 ring, of the C4B2 hexagon and over a boron atom have been preliminarily estimated, the effect of applying the Grimme D2 correction on the adsorption characteristics evaluated, and the comparison of these results with available data discussed. The interaction of two identical Na or K atoms adsorbed at close enough distances (less than 10 Angstrom) is negligible if the adsorption occurs at the opposite sides of the BC3 layer, but creates a steep repulsive potential at distances less than 8 Angstrom if the both atoms are adsorbed on the same side of the monolayer. Relaxation patterns resulting from the two K atoms being trapped at adjacent adsorption sites in the lattice are explained. The results suggest that the density of adsorbed K atoms on BC3 can be interestingly high.