Well, im not realy that knowledgeable on the subject, new bird owner =) But read lots.. Though read knowledge isnt as good as experience. But from what I know, a second bird might help the problem, but you might lose your bond with Tweetie.
I'd try get him to behave with his biting, just keep at it, he'll pick up on it eventuly =D Having one bird that bonds with you but bite is better then 2 birds that dont bond and might still bite. Twice the bite >_<