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The naso I have is almost 2x bigger then the other 2 tangs and is a gentle giant. The clown tang and the chocolate pick on each other a little bit but neither have shown major aggression. I added most of the fish after the tangs in this tank because I had to do a quick transfer and a few of the fish got picked on briefly by the tangs but no real issues
Who is tank boss though? Naso are quite docile but sometimes so much so that a tang 1/3 their size runs the tank and will still reek havoc on new tangs.
Understand that from a tangs point of view, more herbivores means less algae. They've evolved to defend their patch of algae and territory very hard because they may starve if someone else comes in and takes it over. It's literally life or death for them. Angels and other herbivores are occasionally ousted but tangs in particular are often in direct competition for food and will be heckled heavily. The only herbivore that is tolerated (sometimes) is foxface. This is because they're venomous. Even still I've seen tangs stress them to death literally.
With this in mind, your existing tangs are not going to be welcoming. The degree of aggression the new tangs receive can be curbed by a few things:
1) keeping them very very well fed. Keep enough nori in there that by the end of the day it is gone but they have access to it for most of the day. This will make them feel like they need to compete less, but it's no guarantee.
2) re arrange rockwork. This can be successful because the tang feels like they are no longer in their territory temporarily and may hesitate to be as aggressive as otherwise.
3) add multiple tangs at a time. Tangs can take some serious abuse, but 3 on 1 new addition is terrible odds. It may work but the new fish will be very stressed and possibly stabbed several times. Even if only your clown tang heckled the new tang it would not be a fair fight - a fat established aggressive species targeting a fish that has been through h$&@ getting to you and as such has a weak immune system, is thinner presumably because it hasn't eaten as it should, and is very stressed. More tangs will increase distraction and will break up aggression at least by 50%, providing you don't have a tang that singles one of the newcomers out. Powder blue are notorious for picking a grudge and taking it to their grave. Other aggressive species simmer down in a weeks time often. If the fish makes it that long things should get better, presuming they don't succumb to ich or other parasites. But all fish are different and an aggressive naso tang is even possible.
4) use acclimation boxes. This shields the newcomer from attacks from other fish and gets them used to seeing the new fish. It also allows the new fish to adjust a bit so that it is better able to defend itself and know its surroundings better.
5) mirrors placed in the corner of the tank. For a very aggressive tang, sometimes a mirror placed in the corners will keep the fish flashing and attacking itself rather than harassing a new addition. I've personally never done this but have heard of some limited success.
6) removal of the problem fish and a re-introduction later. This can work because the tank pecking order is disrupted. The fish will be confused by the change and work out their own new pecking order and be less concerned with harassing the newcomers. Upon reintroduction some few days or months later, assumedly the new fish will not be the tank boss and will not be as territorial as a result (since it is not his territory now - yet)
Understand that none of this is fool proof. Powder blue tangs in particular are notorious for holding a permanent grudge. Months of time apart will not work if they have a "personal vendetta" to destroy a fish. Not always a tang, either.
Sohal tangs IME are not nearly as aggressive as people make them out to be. I hypothesize that a few people had terror sohal tangs and their stories keep getting repeated by other members and shared with others. As such, they get a worse rep than they deserve because of the same stories being told by several reefers. Honestly I don't even rank sohal tangs in the top 5 or maybe even 10 most aggressive tangs, although it is on my list because I've not owned all tangs
My list is this: (I'm only ranking tangs I've actually had experience with). This is just an opinion after having several of each species over the years in multiple tanks. I will mark how many I have currently of each.
1) powder blue (2)
2) purple (1)
3) Sailfin
4) yellow (1)
5) desjarini sailfin (1)
6) Sohal (1)
7) Clown
8) powder brown
9) Achilles (2) - most are docile but the nasty are up there with PBT
10) Atlantic blue (1)
11) goldrim/white cheek (1)
12) Hippo
13) YB hippo (1)
14 kole
15) Chevron (1)
16) blonde naso (1)
17) Naso
At any point I've had at least 3 or more of these fish for some time, if anyone is curious.
Hope people find this helpful.