Semiconductors are indispensable as the active light-emitting element in many optoelectronic devices. However, even the purest bulk semiconductors suffer from considerable nonradiative recombination leading to low photoluminescence efficiencies. Zero-dimensional quantum dots show a much better carrier-to-photon conversion caused by confinement of the excitons but suffer from nonradiative recombination when assembled into a solid, due to exciton energy transfer. Here, we report on the shape-dependent optical properties of self-assembled supraparticles composed of CdSe/multishell nanocrystals. All supraparticles show stable and bright photoluminescence in ambient up to high excitation intensities. When the supraparticles are deposited on a silicon surface their spherical shape is deformed due to drying. In addition to single-exciton emission, we observe bright emission from multiexciton states at high excitation powers. In contrast, supraparticles that retain their perfectly spherical shape show a spectrum with sharp Mie whispering gallery modes, while multiexciton emission is absent.