Keeping different types of chromosomes long term

[Is this the LFS]

I know that the Viridis variety of chronic will live together no problem. I also know that if atrepictorials(I think that is how it is spelled) are kept together, they will become agrees and the dominate one will kill the weaker. So I’m wondering, are there other types of chromis besides the Viridis that I can keep in a group of 3 or more without them killing eachother? For example the Caribbean blue reef chromis

 

[Retro Reefer]

I have had terrible luck with chromis recently, I have tried three different batches from different suppliers and lost them all to bacterial infections :( I did successfully keep a group of 5 of the blue Caribbeans in my first reef for years with no destructive pecking order.