My female Alexandrine (Madge) flock calls every morning around seven and every evening around six. She goes for about half-an-hour on and off. The male (Barney) doesn't. He just sits there and observes in a humorous sort of way while his little wife gets it out of her system. Then, they eat and spend some time preening each other.
There happens to be a large, slanted roof on a two-storey building at the end of our street and Madge's calls rebound from it, giving her what I can only imagine seems like a 'reply' when she calls. Maybe that's why she does it for so long, thinking she's having a conversation with another Alex? I dunno...
Alexandrines are extremely flock-oriented birds and it's not natural for them to live in isolation. That's why I keep a pair and not a singleton. I can't be with them 24/7 and when I'm not, they chatter away with one another like an old married couple and preen and feed and roost and do all the normal things together.
LOL! I thought Madge's calls were loud and spent a bit of time trying to teach her to tone it down. Then, I got Rosetta the corella and suddenly Madge's calls began to sound like the whispers of angels.
From your description, your bird seems to be making flock calls and searching for another gorgeous green bird in her vicinity. The only way to put a hat on it is to keep the bird permanently with you and provide her with so much 'work' in the form of toys and foraging etc that she won't need to call for company. That's a tall order, though.
Or, you could consider getting her a companion, knowing full well the call-rate might possibly be doubled if they egg one another on.
Points:
i) don't cover the cage in an effort to shut her up (not kind and won't help in the long run)
ii) don't reward the behaviour by going to the cage and interacting with her each time she calls
iii) if she talks, call out to her some of the words and phrases she knows, encouraging her to make different sounds instead of the shrieking
iv) if she doesn't talk, see if you can teach her to repeat some sound, whether it's just a word or a whistle: then, try (iii) above
v) I've had some limited success by feeding the Beaks their veggie rations at the time Madgie likes to flock call. Eating takes up some of that time and keeps her mouth busy.
As I said, once I got Rosetta, Madge's calling stopped mattering against the barrage of sound that comes out of the cockatoo. It really only bothers me now if I'm trying to study. You do get used to it.