Mixing Tangs is always hit or miss. Usually, any initial aggression works itself out, but not always. My biggest concern is how your Sailfin will take to a newer Purple. There is no way to know for sure. It would have been best to add them at the same time. If you try, feed your tank really well a few hours before you start acclimating the new Tang. Then shut the lights off and start acclimating the new fish outside the tank. Leave the lights off until the following morning. The idea being that the other fish will retire to their resting zones and the Purple will have one night to peacefully adapt to your water chemistry and its new surroundings. Then, if the Sailfin does feel the need to prove its dominant position, at least the Purple has had a little time to settle in before enduring further stress. Hopefully, the Sailfin doesn't bat an eye, but its anybodys guess??!!??