The school has been around now 5 centuries. It was founded back in 1603 by Isolde Sayre and her husband James.
It started as small home school were just family friends would come to learn the magic. Few years passed and the wizarding world gets to know about the school. The school slowly began to grow over years. Her current form it gained only 2 centuries ago.
Currently, there are over 5,000 students. Not many but still the school isn't so known as is Hogwarts.
School as always been in the Sayre family and actually, Catherine is from that family line too. She is the heir of Isolde family actually but the last names have changed over years couple of times.
The school didn't have Hogsmeade or even Diagon Alley look like a town for many centuries until it was built around the station a century ago. It slowly keeps growing still.
The school seems to be doing good for now. Even if they have no idea that there is people who want to ruin their little peaceful school. Few years after the wizarding world in England some of the Death Eaters ended up in America. Over years they have found about Ilvernormny too.
There seems to be Gaunt family even who wanna take away the power from current family aka Cheshire.
There could be more bad lurking around the shadows.