The Faceless men are the most dangerous group in GoT
As Arya Stark showed, they could wipe out an entire house if they so choose or even replace that house leader with one of their own and have complete control over it.
https://youtu.be/T1HUAWaxMX8?si=aZBEeFI144gR-Dbe
By taking over enough houses and having a sizeable army, they could choose to take over any region they like and transfer ownership to whoever they please. All it would take is a coordinated effort of replacing the most important Lords with their own agents and then you basically have control over Westero. And given how easily, Jaqen H'ghar took out Ser Amory Lorch in less than 1 minute, without being spotted by any guards, its a rather easy task for them to take over an organization without anyone noticing.