I can never remember what Sublime Text calls its caret/cursor/line insertion above/below command in the key bindings.
On some platforms it is Ctrl + Alt + Up (or Down) and a caret (for typing) appears on the line above (with Up) or below (with Down), but sometimes this fails... and I spend way too long searching for what they call their feature's command.
This is what their docs refer to it as: https://www.sublimetext.com/docs/2/multiple_selection_with_the_keyboard.html