Rats are great pets on their own, but I wouldn't advise letting them interact with a parrot. Mostly because if the rat does bite, which is always possible, it could carry harmful bacteria in it's mouth.
I had a rat named Cloudy and he was the best pet ever (but, of course, I say that about every pet I've owned) he was mega intelligant and was very amusing. He and my guinea pig Rosie got along very well, and we would let them out all the time together. But then one day, for some reason, he bit Rosie. To be safe, we kept them apart afterwards. So, rats are very unpredictable and I don't think that would go well with a parrot.
I had a rat named Cloudy and he was the best pet ever (but, of course, I say that about every pet I've owned) he was mega intelligant and was very amusing. He and my guinea pig Rosie got along very well, and we would let them out all the time together. But then one day, for some reason, he bit Rosie. To be safe, we kept them apart afterwards. So, rats are very unpredictable and I don't think that would go well with a parrot.