Wow! Beautiful tank! What size is that?This will be my last reply because I don't want to go back and forth either. As to adding a purple to the mix. Absolutely not. The only solution I see is removing the PB.
These are my tangs. Notice a difference in the behavior? It's because they all grew up together. IMO it's just asking for trouble adding a 7 inch PB to a 5ft tank with that poor magnificent. I won't bore you with how I feel about animals under my care. I wish you luck and hope things settle down and these two fish become best buds.