Using our nanocavity-based method for precise determination of the absolute quantum yield values, we measure the quantum yield of each of the three different chromophores types with strongly overlapping absorption spectra in a multicolor solution, which is impossible to do by any other existing technique. By measuring the modification of the radiative rate of the chromophores at different cavity lengths, we extract the quantum yield of CdSe/ZnS semiconductor nanocrystals emitting at three different wavelengths and excited by a single wavelength in the multicolor solution. Using several detection channels, we show that only one measurement is needed for determining the quantum yield values of all the types of chromophores in the sample. The obtained results show a very good agreement with the values commonly observed using other techniques. The nanocavity-based method opens up new opportunities of determining fluorescence quantum yields in complex systems and can be used for a big variety of fluorescence studies where multichromophore samples are involved.