Absolutely. You can upgrade the Coop to another Big Coop. You can upgrade any Big Coop to a Deluxe Coop. Then you can build a third Coop, upgrade it to Big and then Deluxe... and a fourth, fifth... as many as you'd like. The more you build and the more you fill them, the more work you'll have managing them, keeping the occupants happy and fed, but if you're up for it. Have fun, mate.
Hahaha, this topic makes me think of the egg farm that another member has. Warning, end-game spoilers, but gosh it's such a great farm with like a billion coops: link