You can authorize. Just make sure you have downloaded anything from your new account you have not that you might want in the next 90 days. This wis only an issue with re-downloading items.
iTunes Store: Associating a device or computer to your Apple ID - http://support.apple.com/kb/HT4627 and - Manage your associated devices in iTunes - http://support.apple.com/en-us/HT204074 - In connection with, "When you turn on iTunes Match, Family Sharing, or Automatic Downloads, or when you download past purchases on an iOS device or computer, that device or computer becomes associated with your Apple ID." "Your Apple ID can have up to 10 devices and computers (combined) associated with it. Each computer must also be authorized using the same Apple ID. Once a device or computer is associated with your Apple ID, you cannot associate that device or computer with another Apple ID for 90 days." - Additional instructions for "Removing an associated device or computer from an Apple ID"