(Option)Alt-Cmd + Down or Up arrow key
From there, you can use arrow keys as normal, but instead of controlling one carrot, you control all the ones you created. So if I use the shortcut key to move to the next word, they all do, same with end of line, or what have you. In the past I had to use regex in my editors to extract quoted text in each line... now I just use multi-select. Each carrot can also be created with the mouse in the Selection menu.
Edit: Apparently it's a feature lifted from Sublime and in other IDEs - thanks!