This is the reason the main pyramid remains relatively unexplored, as in order to discover more they would need to knock down the Church. And that’s not going to happen in Mexico. There are two tunnels that you can walk through and other parts of the archeological site have been excavated nearby.
The Popocatepetl and Izataccihuatl volcanoes loom over the town of Cholula and are usually covered in mist, but we managed to catch a glimpse of Popo before the clouds rolled in. An absolutely spectacular sight and a really nice town for a day trip from Puebla.