In pre-Columbian times, Cholula was a large city and the religious capital of highland Mexico. Construction on the Great Pyramid was undertaken in four stages beginning around the 2nd century BC. It was dedicated to the deity Quetzalcoatl. It is the largest pyramid ever built and is also the largest monument of any kind on earth.
Excavation and reconstruction has begun on one lower side but work is hampered by the existence of a major Catholic Church that was built on the very top of the huge structure. It has been suggested that the pyramid was covered in dirt when the Church was built and that the builders thought they were building on a hill. The argument against this theory is that the geometric pattern of the pyramid structure are very evident even under the dirt cover. Plus this is not the only time the Catholic Church has built on top of and even out of the pilfered materials of others religious structures in Mexico. Tolerance of other Religions and all-inclusiveness is one thing the Catholic religion lacked!
Here is a model of the Great Pyramid complete with the Catholic Church which can be seen on a couple of the photos above. Only the ground structures to the right and the small structure in front have been excavated. Five miles of exploratory tunnels have been dug throughout the rest of the structure. The fear is that extensive excavation will undermine the Church. I know what I would do, but I am not in charge.