In May, Google released a very early preview of the new Google Maps design and then gave out limited invites to play with the new maps.

You no longer need an invite to check out the new Google Maps. You can get it immediately by going to maps.google.com/preview.

Daniel from the Google Maps team said in a Google Maps Help thread:

There are many features you may be accustomed to that are not yet available on the new Google Maps. One such feature is adding a 3rd destination or more to your directions. So keep in mind, this is a preview only.

Forum discussion at Google Maps Help.