Saturation Tweaks per core/game

I was experimenting with consoles, specifically the Mega Drive for now, as consoles tend to be oversaturated, the aim is to get something like the late 80’s muted colors on arcade games, specially for the backgrounds, games like Cabal, Eswat, Bad Dudes, R-Type and more use this style:

I’ve used Gens to isolate the bgs and desaturated the backgrounds, keeping sprites in their original pallets:

Raw:

Desaturated BG:

Raw:

Desaturated BG:

Raw:

Desaturated BG:

Can somebody tell me how to use desaturation among existing shaders, for specific systems, without needing to adjust the monitor settings, drivers, etc, how to add a new pass to achieve something similar to the above?