To reveal its influence on quasicrystal structure analysis, multiple diffraction (MD) effects in a basic Co-rich decagonal Al-Co-Ni quasicrystal have been investigated in-house and with synchrotron radiation. Two weak reflections were chosen as the main reflections (P) in the in-house measurements and 40° ψ-scans of one main reflection have been performed with synchrotron radiation. As well known for periodic crystals and the i-quasicrystal, it is also observed for this d-quasicrystal that the intensity of the main reflection may significantly increase if the simultaneous (H) and the coupling (P-H) reflections are both strong. The occurrence of MD events during collection of a full data set as well as the ψ-scans measurements have been studied based on an average structure model and the kinematical MD theory.