The current launcher version(1.2.2) disables the Play button after the game is launched so the only way to launch multiple instances is via opening the launcher again,
but this will cause the selected profile to have an incorrect session id due to the launcher validating the login when launched.

One way to get around this is open the launcher two times then change the profile on the first launcher and then click "Play" with both.

This is a long way around it, but what I am proposing is that each Profile can its own instance of minecraft.
So to launch multiple version you just edit the profile, select "Launcher Visibility" -> "Keep the launcher open" and after launching the game you change the selected profile and click "Play" again.