I think the main thing you have to realise is that you can process either the M or S part of the signals and after decoding that processing will appear in the relevant part of the stereo spectrum.
It may depend on the mix and where things are and what other things are present. For example I might record a nice acoustic guitar with a M S setup and end up with a nice stereo spread on playback of this part. Now there might be a vocal present. I might decide to scoop the mids slightly on the acoustic guitar in order to make room for the vocals and keep out of the way of the to some extent.
If the vocals are panned centre then the M part of the guitar sound is going to be the right part to apply some mid EQ dip to. This will scoop some mids out of the guitar in the middle part of the sound. But the sound of that guitar on the extremities of the stereo spectrum will not be effected. I might even add some mid or upper top end boost on the S signal and this will effect the guitar sound out on the edges more and that sound will be clear of the vocal sound because you are effecting the L and R hard panned positions a bit more.
You could even use the lead vocal to gently duck the M part of the signal too by inserting a compressor over the M part of the guitar sound and side chaining that from a vocal send. Thus when vocals are not present the mid part of the guitar sound could be made to jump up in level slightly to fill the void left by the vocal. Set the side chain compressor right and you will never notice what the M part of the guitar sound is actually up to.
You could add reverb to the S part of the guitar sound which would only add ambience to the guitar sound at the extremities again leaving the Mid part drier. Or the other way around.
I think just be creative in what you want to achieve in production an know with M S signals you can effect either the Mid part of the stereo image or extremes part of our stereo image independently.