Can you install diablo 3 two times with one disk?

The game should be attaching itself to a battle.net account when you install the first time.

Once there, you can install the game as many times as you want using the same battle.net account, but you can only be logged in once.

Once you tie a game to one battle.net account, you cannot use the same disc to attach itself to another battle.net account.

So the answer to your question is, yes, you can install it twice, but no, you can't play both installs at the same time. If you want to play multiplayer with a friend, you each have to have purchased the game separately.