Nope. In early 2.0 there was a minor bug that allowed you to send a friend request to your alts while they were in a duty, but this has since been removed and is now nearly impossible to do. People who did so before still have their friended alt on their friend list.

The only other way to transfer items between characters on the same account is basically another person handing off from one to the other, or the use of a free company chest (at your own risk, if it's not "your" company).