We report experimental studies of quantum interference of multiphoton states impinging on a two-port balanced beam splitter. When the distinguishability between the two input paths is increased, we observe a reduction followed by a resurgence of the interference visibility in multiphoton coincidence detection. We ascribe this unusual behavior to the competition among contributions from distinct number state components of the interfering fields. Our results suggest that wave-particle duality gives rise to a wide range of largely unexplored phenomena in multiparticle interference.