  In this paper, we present a generic methodology for the efficient numerical
approximation of the density function of the McKean-Vlasov SDEs. The weak error
analysis for the projected process motivates us to combine the iterative
Multilevel Monte Carlo method for McKean-Vlasov SDEs \cite{szpruch2019} with
non-interacting kernels and projection estimation of particle densities
\cite{belomestny2018projected}. By exploiting smoothness of the coefficients
for McKean-Vlasov SDEs, in the best case scenario (i.e $C^{\infty}$ for the
coefficients), we obtain the complexity of order
$O(\epsilon^{-2}|\log\epsilon|^4)$ for the approximation of expectations and
$O(\epsilon^{-2}|\log\epsilon|^5)$ for density estimation.
