My two cents. I've read a lot of "DON'T DO's" about tangs but you almost immediately turn around and see most tanks with multiple tangs mixed in, many in the same genus. Heck, even the BRS160 has two purples. I agree with what some others on here are saying. Tangs are jerks. They will, for the most part, be jerks to one another but somehow it all seems to work out MOST OF THE TIME. There do appear to be those few occasions when a yellow and a purple can't sort it out immediately. Employing tactics to settle this can possibly work/help but it seems this is not nearly as common among all tangs as people seem to say. It definitely helps you have a big tank.
Then people love to say add them all at once. Oh, and also QT all fish. There seems to be a blatant effort to ignore the conclusion that for most (95%?) people this means adding all tangs to a single QT tang of maybe 29gal? Oh but don't keep similar tangs confined in an undersized QT...
Anyways, not trying to rant/offend anyone. Personally, I'd get the fish you want and have a go at it. Acclimation boxes are a good idea. Using diffuser/egg crate to separate tangs to different sides of a tank could help. You may end up having to trap and remove one either temporarily or permanently. But my guess is if you tolerate some jerk behavior while they establish the pecking order, you'll be OK.