Perhaps the Faceless Men and the Iron Bank – both major institutions of Braavos – are actually in league with each other and structurally affiliated?
The Iron Bank is known as the richest organisation in the world, and has enough money to bring down entire regimes. If you don’t pay them back, someone’s going to get you. Maybe a Faceless Man?
The FM don’t flaunt their vast wealth, so where does their money go? Maybe to the Iron Bank, which then lends it out and forces its will on foreign regimes, so that the FM can then continue their influence on the world.
All this would lead to the idea that the Many-Faced God is actually money – like, as in coins which have many faces, but also one face. What did Jaqen give Arya as a token to get into Braavos? A coin. And have you noticed that the House Of Black And White in the opening credits is coin-operated?