Control of color saturation overall is not something that is part of ARCHICAD - it will print (send to printer driver - or PDF) the color values you specify as pen colors, images, or algorithmic shaders. (There is some control of saturation in the rendering engine - but your question is about fills, etc too - so that won't give you what you're asking for.)
You can make a new pen table by duplicating an existing color print pen table and go through it and desaturate every pen... (Double click the pen color in the new table to adjust... and be sure to save the modified table.) This will only address fills, not any surface textures (generated from image files)... But, you can keep your blacks pure black as desired.
If your printer driver has a color setting panel in the print dialog, you can go there and adjust sliders to desaturate the output while keeping high DPI... You might have individual CMYK (or more) sliders ... or an overall saturation slider in the manufacturer's driver dialog.
Or, you can publish your output to a PDF file, and then open the PDF in Photoshop or some other image processing program and desaturate there. (If the goal is to lower the contrast and saturation of all colors but keep black black, then change to CMYK working color space and change only the curves for the CMY inks.).
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