One of the central principles of quantum mechanics is that if there are multiple paths that lead to the same event, and there is no way to distinguish between them, interference occurs. It is usually assumed that distinguishing information in the preparation, evolution or measurement of a system is sufficient to destroy interference. For example, determining which slit a particle takes in Young's double slit experiment or using distinguishable photons in the two-photon Hong-Ou-Mandel effect allow discrimination of the paths leading to detection events, so in both cases interference vanishes. Remarkably for more than three independent quantum particles, distinguishability of the prepared states is not a sufficient condition for multiparticle interference to disappear. Here we experimentally demonstrate this for four photons prepared in pairwise distinguishable states, thus fundamentally challenging intuition of multiparticle interference.