We propose a novel scanner characterization approach for applications requiring color measurement of hardcopy output in calibration, characterization, and diagnostics applications. The method is advantageous for common practical color printing systems that use more than the minimum of three colorants necessary for subtractive color reproduction; printing with cyan (C), magenta (M), yellow (Y), and black (K) is the most prevalent example we use in our description. The proposed method exploits the fact that for the scenarios in consideration, in addition to the scanner RGB values for a scanned patch, the CMYK control values used to print the patch are also available and can be exploited in characterization. An indexed family of 3D scanner characterizations is created, each characterization providing a mapping from scanner RGB to CIELAB for a fixed value of K, the latter constituting the index for the characterization. Combined together, the family of 3D characterizations provides a single 4D characterization that maps scanner RGB obtained from scanning a patch and the K control value used for printing the patch to a colorimetric CIELAB measurement for the patch. A significant improvement in the robustness of the method to variations in printing is obtained by modifying the K index to utilize the scanned output for a black-only patch printed with the corresponding K value instead of directly utilizing the control K value used at the printer. Results show that the proposed 4D scanner characterization technique can significantly outperform standard 3D approaches in the target applications.