How can I expand multi-line selection to full lines in PHPStorm?

With WebStorm 11 (at least) the multi-caret keyboard shortcut is:

Ctrl then Ctrl+Arrow Up (or click & drag with the middle mouse button/scroll wheel)

then to select the full lines:

Home then Shift+End

which you could even create as a macro with a keyboard shortcut.

I used to accidentally activate the multi-caret all the time (I scroll with Ctrl+Up/Down), so I knew how to do part of it, but it took me ages to figure out that extra Ctrl tap at the beginning.

Update

Nowadays (welcome 2020) Go to Preferences > Keymap. Change or add the value to Add Carets to Ends of Selected Lines => CMD+SHIFT+L to have it behave like Sublime Text so it looks like

Old Answer This is as close as I could get it (before 2020):

Go to Preferences > Keymap. Search for Clone Caret Above/Below.

On a Mac, it looks like this

The keys are:

CMD+SHIFT+CTRL+ARROW_UP for Clone Caret Above

CMD+SHIFT+CTRL+ARROW_DOWN for Clone Caret Below

Click on Apply and it will work