Lots and lots of people do it, but it's unlikely they will ever be friends.
Here is a link to a grey whose top beak was bitten off by a cockatoo: http://centerforavianrehab.blogspot.com/2007/07/this-is-jackie-one-of-our-frequent.html
If she does decide to get another bird, I'd recommend that she get one (adopt an older bird from a shelter whose personality is more apparent and who picks her) with the understanding that not only may they not get along, but they may hate each other.
I had a caique (who passed away in 2014) that didn't get along with any of my other birds. They would dive bomb and attack him, so I had to take extreme measures to keep him safe. Due to the fact that they were all similar size, nothing tragic happened (supervision can't prevent everything) but the worst that happened was one bird escaped from his cage, went over to that bird's cage, and they apparently had a battle through the cage bars. They both healed, but were obviously in pain, and I was stuck with a $1,000+ vet bill.
Thank you for thinking seriously about it and not getting another bird on a whim. I know my first bird wishes she were still an only bird. She is likely to outlive her current companion (they coexist -- have been living together for 12 years now and pretty much ignore each other.)
Greys live in single-species flocks in the wild, so they tend to not be as friendly to other species as, say, nanday conures.