I currently have a case with only one fan port in the back, which I am using as an outtake fan. My gpu is a 1080 and under load runs at about 83 degrees. If I buy a case with more fan ports, so I can get better airflow, is it likely I can get this down below 70?
Yes. Air flow is very important to keeping temperatures low. Find a case that supports a couple of fans at the front and a couple at the top. You may have to buy fans separately and install them.
I'll suggest that you improve the air circulation within your case, first. There are accessory fans that plug into expansion slots, and can move air directly onto your GPU. Something like that made a big difference in one of my towers. There are also accessory fans that duct through the back panel expansion slots.
Either would be a lot cheaper than replacing the case, and easier to try.
The location of the tower play a role as well. The area needs to be well ventilated. U can try adding a hydro cooling system but more fans should work too. (room temperature plays a role too.)
case fans won't make a 13 degree difference for a gpu. it may help slightly, but it won't make a huge difference.