Is There a Way to Add Tabs in Global Fields?
As far as my knowledge goes there is not a way to do this without some though changes.
Wouldn't it just be better to add another global and just name it settings?

Something like:

globalSettings(option1)

globalSettings(option2)

globalSettings(option3)

So that you organize them like that? Only thing you have to keep in mind then is when you use it in your template you have to keep track of which setting is used for what but if you name them right that wouldn't be an issue.