https://www.wayfair.com/pet/pdp/arc...oor-chicken-run-with-mesh-cover-aosc1611.html
So I'm using that link, which you previously gave, to look at the prefab run.
I see it has an opening in one end--are you saying that is smaller than the door of the existing run?
Does it work to leave off the entire end panel of the new run, thus making a bigger hole in the end?
Or if you have some chicken wire or hardware cloth, you can put the new run a short distance away, and use the chicken wire to connect them together. The open door of the existing run could even be one side of the connection, leaving just the other side and the top to deal with.