Add Save & Increment function to the File Menu

My idea is to add a Save & Increment function to the Blender File Menu.

Long story short, I use Blender a lot for work and end up having many, MANY versions of files. Currently, it take four clicks to Save and then increment the file (File > Save As > Increment +- > Save As). Having an option to do it automatically would bring this down to two clicks (File > Save & Increment). I know it doesn't seem like a lot, but the four clicks gets real tedious when you're on version 54, 55, 56... etc.

Please forgive me if I'm an idiot and there already is a faster way to do this, or a python script/addon. Just haven't noticed any and think this makes the most sense. Cheers.