I started out as single GCC mom, and we did great. But I found my second GCC 10 years later and added her, both were DNA girls. They loved each other instantly. Spent 7 years mostly living in the same cage, but occasionally had to live side by side cages when issues came up.
Then my flock grew , and I say my burds are much happier with friends. ( currently all caged separate, but spend the day out together) But I've heard so many other struggles and unhappiness with more than one.
With later additions I took it very slow..after QT. I had cages on opposite sides of room. Tip, never allow a free bird to land on a caged birds cage. I would hang out with original birds next to new burd still in cage. And just give everyone treats. We did that lots till everyone thought it was no biggie. And I would hang out with new bird by the caged birds and give everyone treats. I did a lot of walking one burds over and say hi to a caged bird and treat. I payed lots of extra one on one time with original burds ( especially whomever seemed a little jealous.
When it seemed everyone excepted that a new burds was in the home. I kept moving the new burds cage closer to all my other cages but no closer than 4 feet at first.
I set up a meet and greet buffet in a neutral location. I use my breakfast bar , with a non slip towel on top. Set up several yummy food location spread out. Then I kept an envelope handy incase I needed to block any charges. I got each bird in a happy calm mood and placed them spread out at yummy food stations. I got the new burd and brought over also in a happy calm mood. And set it far away from the others st at a yummy food. If anyone acted up I pit them back in the cage and tried again later. Its very important to prevent s f fights or charges. I did this often till they could eat together as a flock. I allowed them to meet on their own terms when ready.
Some birds took years to form friendship. But knew to behave and give space. Some birds dislike each other but give space and behave. Even the birds thst dislike each other can all be on me at the same time. Because they know any misbehavior and the go back to the cage for a few minutes or I move them to one if the play stations. And they really want to be with me.
Well that was long, hope it was useful!
The people I know who things went south rushed it, put burd on the sane perch together. And had fights happen with first meeting. First impressions matter, and burd can hold grudges. But even mine with grudges could evolve older time with management and even becoming best buddies ( but took a year or two)
So at least for me the short answer is yes. Even burds thst don't get along seem to benefit from having another around. But I have others disappointment and stress in handling birds that hate each other.