Based on the Gray col try this
Linerize your CTP plate maker
Run set a plates using 100 percent and 50% screen of CYMK
Run ink density to your agreed apon density
read your dot gain for each color
K should be 20%
C should be 19%
M should be about 12%
Y should be about 12%
make adjustments to your output device to make the printed pice match these numbers
Do this for each press. and for each paper type coated and uncoated. If possibl make a color bar that incude a CMYKand a Neutral color built with 50% C 40% MY. This will give you a good match standard that I have found to print Very nice. Not true graycol process but a simple process a small or inhouse like myself can do and get great results.
good luck