I just found this out this morning! It applies to both USTA and ITF events per Friend At Court.
Players may enter two tournaments which occur at the same time if they receive permission in advance from both tournament directors in writing/email. This is not a new rule but is one that has not been reported on every occurrence in the past. Most tournament directors will approve if asked before the entry deadlines. Once entry is gained in one tournament, you should then advise the other tournament to remove the player from the active alternate list. You will forfeit the entry fee.
This is great information to have, especially if your child is going through the Alternate List Blues. However, please note the part about forfeiting your entry fee – those can add up!