Gamut compression is to map the larger gamut of original to the smaller gamut of destination in color digital printing. To guarantee high quality of reproduction, color match is required to be done as well as possible. We can expand the destination gamut by using different methods, for instance, improving paper properties, improving printing technologies, selecting better inks and adopting high fidelity color printing technology which uses more than 4 inks (i.e., 4 + x) to print. In this paper, we performed experiments and theoretical studies to verify the process using CMYK and spot colors model to achieve HF color printing. The color gamut characteristics of the above model, CMYK and spot color inks, were analyzed. We also studied the theoretical basis of spot color selecting methods and the influences of various methods on expanding destination gamut, which included using different color gamut mapping methods, using novel halftone technique, adding new primary inks and selecting suitable papers. Experimental showed that the range and result of destination gamut expansion of the above methods were different. Using modified screening methods and more than four colors printing, 4+x high fidelity printing could achieve the best optical effect of printing image.