  In this paper, the strong existence and uniqueness for a degenerate finite
system of quantile-dependent McKean-Vlasov stochastic differential equations
are obtained under a weak H\"{o}rmander condition. The approach relies on the
apriori bounds for the density of the solution to time inhomogeneous
diffusions. The time inhomogeneous Feynman-Fac formula is used to construct a
contraction map for this degenerate system.
