We study the charge transfer of the multi-electron collision system Li$^{2+}$ + Ar using the time-dependent density functional theory non-adiabatically coupled to the molecular dynamics. By implementing the particle number projection method, the single- and double-charge transfer cross sections are extracted at MeV energies, which are in good agreement with available experimental data. The analysis of charge transfer probabilities shows that for energies higher than 1.0 MeV, the single-charge transfer occurs for a broader range of impact parameters, while the double-charge transfer is dominated by close collisions. To gain the population of captured electrons on the projectile, we compute the orbital projection probabilities. It is found that the electrons of the Ar atom will most possibly transfer to the $2p$ orbitals of the Li$^{2+}$, and only a small portion of captured electrons distribute on the $s$ orbitals. This work verifies the capability of the present methodology in dealing with charge transfer in dressed ion collisions at MeV energies.