Yes, you can only get a 3 month visa, you can't get a new one just by going to Peru anymore.
You could get a x-20 visa where after paying over 200+ you get another 3 month extension.
Now if you become a part time teacher, buddy of mine used to teach for a couple of hours here and there, he got a work visa, and he was able to stay for 9 months. Good luck.
