The only species of Cichlid I have managed to keep in a group are Angels or Discus but I have never had a tank larger than 3 foot-ish and eventually the Discus fell out. This was possibly because they are initially shoaling fish when in the river but when they breed its in small land locked pools which they will defend. Doing a water change or feeding live food would often kick them into breeding mode which caused fights although they are not as bad as some at going to the death if other fish stay far enough back this will do them, others some central Americans will chase and chase until the other Cichlid has no choice but to hide away often weakening the fish and possibly succumbing to disease stress related.
Cichlids are often seen in the shop in groups in a small tank convincing people that they will be al right together. In the shop there is no good breeding areas, they are often young or immature fish and the fish put up with each other for safety because there is no where to hide they go for safety in numbers. Once in the tank their mind set changes, the fishes only two goals every minute of the day are feed and breed. Seeing somewhere nice to breed it now thinks I need to get rid of any fish that can eat my young so will chase them and another same species fish is a total threat that can stop it breeding altogether.
Species and tank size are the clincher here, some species will mate with any female some pick a female and stick with it for life so adding just a male and female still might not work.
I find dither fish can help in some of the less aggressive species, lots of fast moving shoaling fish Harlequins/Tiger Barbs can cause enough distraction to prevent bullying.
I keep a pair of Blue Rams which are known as some of the least aggressive but on a bad day I've seen them coral Angels 4 times their size into a corner
🙂 When the eggs have been either ate or the fry sucked in the filter the female will often chase him for his life for a couple of days but when the need to breed again comes round she soon gets over it.
Aquariums imitating life I suppose