I have a Red Sea Purple tang and a Red Sea Sail Fin. I added a yellow Tang and they beat the out of him. I started with the purple tang and added the sailfin with no incidence.
I have 5 yellow tangs. I thought of adding a purple tang, but was told by LFS that the 5 would beat up the single purple. Everything I read advised that unless you have a big tank, you need to introduce different species of tang at same time.
Book also advised that best to keep tangs either as a single or in packs of 5 or more. That way if one dominant one, he will have more fish to pick on instead of beating up on just one other fish. If your tank is big enough you could bump up the # of tangs, if you prefer to have that many tangs. Or try to remove the yellow you put in and take back to LFS and exchange for some other fish. Other may say/agree that it might just take a few days for Purple to establish dominance and then it will back off the yellow. Hope it will survive long enough for that to happen. How much tail fin has yellow lost? Any trouble for fish breathing?
I've also read that tangs of similar shapes or colors may fight. A Purple and a Yellow are definitely similar in shape. I keep a black long nose tang and a hippo tang. They took to each other immediately and swim and graze together without and conflict at all. When I added a Copperband Butterfly the black tang went after her. Could have been the long nose and somewhat similar shape. The hippo did not bother her(exactly the opposite of what I expected). The black tang and CBB are fine together now but it did take a few days for the tang to accept the intruder.
Tank size could also be a factor you might want to consider. Purples and Sailfins can get pretty big. Unless you have several hundred gallons it could get pretty crowded very soon, especially if you add another tang.
