I'm no high ranking member of the "Tang Police" or anything, but I like to think I know a few things about them...
I agree that your tank is too small for 4 tangs...in a bigger tank you'd be all set. Not to mention you are going to have problems with the 2 yellows at some point or another. (I also am one of those that believe NO tang should be in a 4 foot tank, no matter how small it is or what your future plans are - sometimes those future plans don't work out and then the poor fish is stuck in a tiny home.)
I also had to respond for the fact that I think the Powder Blue wasn't getting his due props in this thread. IMO the Powder Blue can hold his own...especially with a Purple Tang. It is all about who was added first though. If you have an established Purple and add a Powder Blue to a small tank then yes, the Purple may dominate. The Powder Blue will be stressed to begin with, being added to a new home, possibly just being shipped across the globe, he doesnt know his surroundings, scared etc...
Now have the Powder Blue established and add the Purple...
It would be the exact opposite.
Just to throw this in there, I know a guy that had 21 Tangs in his 7 foot 265 gallon tank. He couldn't figure out why they wouldn't get along.

He's down to 7 or 8 or so. He had a school of yellows, a purple, clown, powder blue, achilles, naso etc etc. :mad2: