They would all be fine together but the clown is a big fish, it needs a big tank, at least 2000L for long term but if you're planing on moving it on when it gets too big then fine. If it was me I would go with a powder blue instead just because it won't get so big
The purple and yellow are closely related so aggression can occur. I'd get small specimens and add together if possible to avoid any fighting over territory. Also feed lots of algae, as this helps reduce aggression.
The clown tang gets big, and needs a very large swimming space, tank size is recommended to be 1000l minimum. Although you would get away with a smaller tank with a small specimen for a while, you would eventually need to either upgrade or move on, either of which would mean disrupting the tank, as catching a tang in it's own territory would not be easy so you would probably end up deconstructing your tank to do so risking crashing the system.
Personal experience....I would stay away from the clown Tang as they usually become pretty vicious, I had one and it knocked 7 shades out of everything in my tank till it picked on my foxface and needless to say it was dead the following morning, the other 2 are both part of the zebrasoma family but if added together and young they will be fine
I’ve had a purple, a yellow and a mimic in the same, only issues for a few days then they settled, however these were relatively small fish when I added,
Tangs are massive jerks. If you have to get a herbivore, a fox face is pretty chilled. Clown tangs attract parasites, they have thin slime coats like powder tangs, so try and quarantine it for a reasonable amount of time.
