It really shouldn't be difficult and it's a great feature to have (that was there in 9.x).
You create the additional setting in the Management Interface:
This would in turn create a new icon using the font.awesome icon you selected inline with the other icons:
This diagram would show the float space of the other icons:
Green is the space where the default icons live and blue is where the custom links would live and overflow too. This would allow various portals to look fundamentally different. Right now, every 10.x and 11.x portal looks like a clone of the other... There's no personality.