In this paper, we consider the design of a reduced-rank minimum mean-squared error (MMSE) combiner in an asynchronous multicarrier-direct sequence-code division multiple access (MC-DS-CDMA) system. It is shown that the combiner weights are related to quantities whose expressions resembles the eigenvalue moments of the interference autocorrelation matrix. To lift the burden of recomputing the weights from time to time, the weights are evaluated in a large system regime and averaged over random parameters including asynchronous delays, correlated fading coefficients and spreading sequences. Explicit expressions for the asymptotic weights of the MMSE combiner are derived. The large system setting is with the spreading gain N and user number K approaching infinity, but K/N = β and the number of sub-carriers both finite.