1. A color image processing apparatus comprising: an image forming unit configured to form a color image using recording materials of a plurality of colors; an image processing unit configured to implement a plurality of image processing methods that achieve a plurality of types of halftone representations; a color measurement unit configured to perform color measurement of the color image formed by the image forming unit; a multi-color calibration unit configured to execute multi-color calibration by causing the color measurement unit to perform color measurement of a pattern image including a plurality of multi-color patch images having colors different from one another, each of which is formed using multiple color recording materials by the image forming unit, and then acquiring, based on results of the color measurement by the color measurement unit, correction data to be used to bring a reproduction characteristic of a multi-color image formed by the image forming unit close to a target value, wherein an image processing method used to form the pattern image including the plurality of multi-color patch images during the multi-color calibration is one specific image processing method among the plurality of image processing methods.