My feeling is that you should start from the press and work your way back. Run all 4 colors at levels that produce a consistent ink film thickness on the rollers. This ink film thickness should be even across the width of the press, and a thickness thats able to run stable, free from washing out, yet resistant to dry ups. It should be app. the same from unit to unit. It should be a thickness that has solid areas looking rich, yet not so dense that the sheet wants to set off. Once you've arrived at this stable ink film thickness then the printed sheet should be evaluated and any further corrections made in pre press. It should be noted that you can actually measure the ink film thickness with ,believe it or not an ink film thickness gauge. Some refer to this gauge as a Peto gauge. The temptation to make jobs happen on press should be avoided whenever possible. If colors are not matching then its time to get new plates with corrections from the pre press dept. If you strictly adhere to these suggestions you will find your presswork to be more consistent regarding color matching, color control throughout the run, and minimizing defects like dry ups, wash out, offsetting, etc.
If you do not have someone in your company thats capable of leading you through this very technical process of "fingerprinting" then I would suggest either hiring someone full time, or at the very least calling in a consultant fully familiar with the entire process.