Press Shift+Alt and click the LEFT mouse button at the location of the caret.
Double-click Ctrl and press up arrow or down arrow keys.
On OSX it seems to be enough to press down the LEFT-ALT and add new carets with mouse LEFT CLICK, or press down SHIFT+ALT and paint the cursors with mouse.
Another option: with text selected, toggle column selection mode:
The default shortcut to toggle the mode is:
Linux/Windows: alt-shift-insert
Mac cmd-shift-(numpad) *
(or Edit→Column Selection Mode)
It's an inconvenient shortcut for Mac, as most laptops have no numpad. I remapped it to cmd-shift-8.
Column selection mode actually has other purposes too: it changes the default behavour when selecting text with the keyboard and mouse. Toggle it off again to return to normal selection behaviour.