No, you cannot authorize on a different account. they are tied to the account that purchased them. Now, I have called Apple iTunes Support before in the past and gotten a human so you may be able to talk to them about changing the music to another account but I wouldn't hold out much hope for that.
That being said. I believe, that the iTunes store can be authorized for one account but if you want to play music from another account you can do that and it doesn't tie it to the iTunes store. So, that option can be there, I guess. Simply authorize the music but don't tie the store to the your account. If you do that, I believe the account in the iTunes store needs to be setup first within iTunes before you authorize on the other account. It may not matter but I wanted to put that out there.