When I was first grappling with the concept of M/S it helped me to use the other common naming, Sum and Difference, where sum is mid and difference is side. When you have stereo signal, sum is what is same in each of two channels (L and R) and difference is their difference. all width information is in that difference channel, so if you boost it, it exaggerates width and if you lower it, that narrows it.
It is really useful to use MS encoder and decoder plugins in chain and put any other plugin between them. Just remember to connect only 1st pin ins and outs for mid processing (so channel 2, the side bypasses it) and only connect 2nd pin ins and outs if you want to process side.
Remember that on their own two M/S channels are just two mono channels, and that side channel is usually pretty phasey and funky sounding on its own, but when you combine them with M/S decoder processor, the result is beautiful L+R stereo
