Select them, open the tag editor and then tag inspector. Then you can edit the specific value you want without disturbing other tags. Just beware that if you've selected any files without that tag, it will be applied to them, too.
If anything is going to be done related to this, it would be good if an 'add tag' feature would be added to the tag editor panel.
Especially for genres it makes perfect sense you would want to be able to simply add a tag without being worried that that action might delete existing tags.
Same for 'keywords'.
The fact that you can not do that in a tag
editor, but you need to navigate to something called tag
inspector isn't logical, nor intuitive, and not many users will find that by themselves.
As a secondary improvement—trying to imagine what the op intended—it might be nice to have a pop-up panel showing all genres and the category that they reside under, and make a genre clickable so to add it.
But that might be a bigger challenge to dress up nicely in the user interface.
(Also because users may be using their own customized genre/genre category list, and the amount of genres and categories will differ because of that.)
edit,
Giving the second part some more thought:
A practical and useful implementation could be that when you click 'add genre', the initial panel that pops-up would only contain your genre categories, and after you selected one, it would delve down and only display the genres that fall under that category.
As a rough indicator that might be helpful in defining some parameters:
If I am not mistaken, by default MusicBee has defined 21 genre categories, and the largest amount of genres that reside under one category is 119.
I have my own customized list, containing some 50 genre categories, and the largest amount of genres that reside under one category is 66.
Such numbers would be difficult to handle in a single panel, but probably not that hard in a two-step interface.
I don't know if this is what the op had in mind, but I myself would use an 'add genre' feature implemented like this for sure.