Playing as brazil, I have declared war on venezuela and peru. Venezuela isn't doing much, I've taken one tile but nothing is really happening there. Peru was difficult, I had some initial success pushing in, making Peru very skinny. However, Peru managed to take to push to become HUGE. I then declared war in Bolivia and quickly took most of its territory, but Peru pushed me out. Even with ~100 divisions working together, I can't seem to defeat any of Peru's divisions.
O, man, that is so easy to do. There is a reason I picked artillery as my example. I have done exactly that more times than I can count.
That said, artillery is named king of battle for a reason. If you can get your artillery production bulked up, you can massively upgrade your force.