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In this paper, we prove pathwise uniqueness for stochastic systems ofMcKean-Vlasov type with singular drift, even in the measure argument, anduniformly non-degenerate Lipschitz diffusion matrix. Our proof is based onZvonkin's transformation \cite{zvonkin\_transformation\_1974} and so on theregularization properties of the associated PDE, which is stated on the space$[0,T]\times \R^d\times \mathcal{P}\_2(\R^d)$, where $T$ is a positive number,$d$ denotes the dimension equation and $\mathcal{P}\_2(\R^d)$ is the space ofprobability measures on $\R^d$ with finite second order moment. Especially, asmoothing effect in the measure direction is exhibited. Our approach is basedon a parametrix expansion of the transition density of the McKean-Vlasovprocess.

Strong well-posedness of McKean-Vlasov stochastic differential equation with H{\"o}lder drift