It is possible. I have a Barred Rock who has laid 2 eggs in a day. Not often, but a few times.
I got 2 eggs, I think, today, from her sister. But it is a worry. I believe the first one was stuck in her oviduct. She tried to lay yesterday a few times and was unsuccessful. But when I went to let them out of their coop at 6:00 a.m. this morning there was an egg in the nesting box-- an odd one, with a chalky ring on one side and discoloration on the end. Intact, not soft.
Then at about 2 she was on the nest again and I got another egg. This one had no chalky ring, but it did have an area of discoloration on one side.
I am worried she might have Egg Yolk Peritonitis. She didn't have the suffering symptoms of Egg Binding, that I could see, and she is out and about this afternoon and even ran. However, she's panting hard (it is somewhat hot). I suspect she may have an underlying disease, due to the panting symptom. Her sister doesn't pant as much. I hope I haven't overfed her. Fat chickens tend to have these kinds of troubles laying eggs. That's why I took her off scratch in the spring. She has pecked out a bunch of her breast feathers, which could signify Fatty Liver Disease.
So many maladies to worry about. She had black spots on her comb recently which is a sign of Fatty Hemorrhagic Liver Disease, but they finally went away. I thought maybe it was because I let her out to free-range for more exercise and greens in her diet. But now this stuck egg is a new worry...
Good luck with your chicken. She sounds very special.