t seems to me that the question is whether a Bartlett's and a squammi or a square will get along
I don't know about the square, but I would hesitate to put a squammi & a smaller anthias like a Bartlet's in together alone as the squammi may spend all his energy aggravating the Bartlett's anthias
If you put 2 similarly matched anthias like bicolor and squammi, it could work out better similar to grouping aggressive fish they are tough enough to "take it" from each other - but might overpower more gentle fish
You could try it, maybe they''ll be buds - I wouldn't expect the Bartlett's would be murdered or anything and if the aggression got bad, you should have plenty of time to remove one of them