  We study the asymptotic behavior of the normalized maxima of real-valued
diffusive particles with mean-field drift interaction. Our main result
establishes propagation of chaos: in the large population limit, the normalized
maxima behave as those arising in an i.i.d. system where each particle follows
the associated McKean--Vlasov limiting dynamics. Because the maximum depends on
all particles, our result does not follow from classical propagation of chaos,
where convergence to an i.i.d. limit holds for any fixed number of particles
but not all particles simultaneously. The proof uses a change of measure
argument that depends on a delicate combinatorial analysis of the iterated
stochastic integrals appearing in the chaos expansion of the Radon--Nikodym
density.
