It is quite possible to mix Anthias of different species (they mix in nature quite often). The trick is the right combination and introduction order
It would be best to introduce them all at once or the smallest/most timid anthias first. The downside to adding them all at once is the sudden increase in the bio-load. Most systems cannot handle it unless they are large (240+ gal).
An example of introduction order would be (only one male per species):
4 Dispar
4 Lori's
4 Bi-color or Bartlett's
4 Lyretail
The males of the above will spar and chase each other but if there are plenty of hiding places they will do OK.
The species I've had trouble with being too aggressive are:
Squarespot
Redbar/tri-color
Redcheek/Green
Regards,
Kevin
Note: I do not want to mislead anyone into thinking that Anthia species are easy to keep they are not but for me they are one of the most beautiful and interesting fish in the hobby.