Based on the difference between multi-primary displays (MPDs) and three-primary displays, we propose a new definition for evaluating the color gamut volume (CGV) to explore the upper limit of MPDs, which could theoretically represent all colors that MPDs can display. The proposed definition corrects the defects in the L*a*b* color space that arise when calculating the CGV of MPDs. In view of the high computational complexity of this method, we propose a simplified scheme with a small margin of error. Additionally, we verify the new definition with experiments on a six-primary projector. This method is helpful in guiding the selection of light sources and the evaluation of MPDs, and also has great reference value to calculate the target gamut for gamut mapping in MPDs.