I have two bigger birds - not as large as Amazons or Greys but certainly larger than budgies. I got Leia in 2017 and we rehomed her younger sister, Kira, in 2022.
Both were initially raised by their parents, then handfed and raised with their siblings and allowed to interact with other Pionus. I very specifically sought out a breeder who did not pull chicks too early. Leia stayed with her breeder and other Pionus until she was nine months old and thus is more aware that she's a bird - she's more independent, confident and knows what she likes. Kira was originally homed at a more typical age i.e. once the breeder was confident that she was fully weaned. Her first owner had her on his shoulder for most of the day, and as such Kira is clingier and really, really wants to be on a person.
I once boarded Leia at a parrot hotel with resident Greys. When I picked her up, the hotel owner commented that "she doesn't like to share": cue mortification much like when you pick your child up from nursery and get told that about your kid! I can only imagine she tried to pick a fight with a bird nearly twice her size... So I knew that she probably wouldn't immediately buddy up with a new bird, but I hoped that she would tolerate a second.
Happily for me, they do tolerate each other. Kira would like to be friends, but Leia does not want to be friends. We give them as much space as we can so they can fly away from each other, and we offer lots of perching opportunities so they don't have to argue over them. Leia will chase Kira off and they do sometimes open-beak spar with each other, but no one gets hurt.
They do engage in parallel activities like eating and preening. They have been observed to share the tree so fingers crossed, they might one day mellow out like Kobe and Ollie.
Leia is much more fluent in parrot due to her upbringing, whereas Kira kind of invented her own Cool Noises. Interestingly, Kira's calls have changed and have become more like Leia's. They get pretty loud together and do set each other off: if one starts having a bit of a shout, the other quickly joins in.
For me, the main challenge in having two birds rather than one bird has been one of space. Finding space for two 100x80cm cages is a challenge in a small London flat! This is the first place we've lived that we physically had room for two cages. I think it's also harder to manage if you have two big birds who don't like each other. Their space requirements mean that it would be difficult to give them both enough time and space for individual out-of-cage time. A budgie can happily zip around in a small room, whereas that room feels rather cramped with a bigger wingspan.
I would love to have a larger flock, but again, space is the limiting factor.
Personally, I think larger birds should have an upbringing that lets them know that they are birds. I would love it if big birds had the same opportunities for socialisation into a flock and learning "bird culture", and had bird companions throughout their lives. Perhaps part of the reason we perceive larger birds as being choosier is because they aren't necessarily as well socialised: there are only birds that they really really like (friends) and birds that they really really don't like (enemies), and they don't necessarily have the social skills to navigate social relationships with birds that are in-between.
In a flock, there are going to be birds that are closer and birds who are more distant: I suppose the human parallel to that is navigating interactions with colleagues: we may not count them as friends but we may not dislike them, and it takes social skill to negotiate relationships with individuals that are more distant to us. Like I think my colleague Olli is okay, we've worked together on a project, I think we can trust each other to get the job done, but I wouldn't say we've clicked: we probably both find the other a bit aloof, we don't seek out each other's company and wouldn't interact outside work. That, for me, is a trickier relationship to navigate than an actual friendship, and it takes practice to develop the skills to have a cordial relationship with people with whom you work but don't click with. I think there are parallels to that in a flock, and that our birds don't necessarily have the skills to navigate that kind of interaction.