OH!! I didn't quite catch that in your OP (the screenshot helped clarify). I thought you just wanted to change the way the current "GROUP" value is stored in the text file, not add a new value! So what you're wanting to do is be able to change the DEFAULT "Group parameter under" setting for each of your shared parameters in the same way that if you make a "Length" parameter, it's grouped under "Dimensions" by default, "Text" goes under "Text", etc.
So, for example, if you had a "Yes/No" parameter called "Show Plate" in a custom "Truss" Parameter group (the current "GROUP" column) in your Shared Parameters file, you could set a value for "Group parameter under (default):" of "Graphics" (per the attached mockup below), so that when the parameter is brought in to your project, it would automatically go under "Graphics" (instead of "Other", which is the default for "Yes/No" parameters). In addition, this new value (maybe called "DEFAULTGROUPUNDER") would be set by plain-text values (in the Shared Parameter text file) that correspond to the values available in the "Group parameter under" list. If there is a typo in the file, Revit should throw an error referencing the line number, or should just put it under "Other", or whatever the default "Group under" would be for that variable type (since, unlike the "GROUP" value, which is just a housekeeping tool, the value in the new "DEFAULTGROUPUNDER" would need to correspond exactly to one of the OOTB groups).