  We prove the well-posedness of some non-linear stochastic differential
equations in the sense of McKean-Vlasov driven by non-degenerate symmetric
$\alpha$-stable L\'evy processes with values in $R^d$ under some mild
H{\"o}lder regularity assumptions on the drift and diffusion coefficients with
respect to both space and measure variables. The methodology developed here
allows to consider unbounded drift terms even in the so-called super-critical
case, i.e. when the stability index $\alpha \in (0, 1)$. New strong
well-posedness results are also derived from the previous analysis.
