According to the Twelfth Doctor, they had offices in every capital city on Earth. Specifically, these locations included Washington and Tokyo, with the corporation's main headquarters being in New York City.
The Twelfth Doctor and Nardole visited the New York and Tokyo branches of Harmony Shoal in the early 21st century. They discovered that the corporation was in fact a front for the Shoal's plot to extract the brains of key world leaders. The Shoal planned to blow up New York City using a rigged spaceship to show that Harmony Shoal's headquarters was the only building capable of withstanding the impact. Authority figures would have then turned to them for safety and security, at which point the Shoal would have replaced their brains and, using the world leaders as puppets, prepared the Earth for full colonisation.
The plan was thwarted when Grant was able to stop the rigged spaceship before it could cause any damage. Harmony Shoal was then shut down by UNIT after a tip-off by the Doctor. A UNIT agent became the current host for the Shoal that had formerly inhabited Dr. Sim who managed to change hosts when UNIT invaded the corporation's headquarters. (TV: The Return of Doctor Mysterio)