  We study the impact of distinguishability and mixedness -- two fundamental
properties of quantum states -- on quantum interference. We show that these can
influence the interference of multiple particles in different ways, leading to
effects that cannot be observed in the interference of two particles alone.
This is demonstrated experimentally by interfering three independent photons in
pure and mixed states and observing their different multiphoton interference,
despite exhibiting the same two-photon Hong-Ou-Mandel (HOM) interference.
Besides its fundamental relevance, our observation has important implications
for quantum technologies relying on photon interference.
