Considering that a Faceless Man is "no-one" and can change appearances at will, is there any mention of how large their order actually is?
For all we know it could just be two people: The Kindly Man and Waif....
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In A Song of Ice and Fire, Arya attends a meeting of eleven Faceless Men:
Eleven servants of the Many-Faced God gathered that night beneath the temple, more than she had ever seen together at one time. Only the lordling and the fat fellow arrived by the front door; the rest came by secret ways, through tunnels and hidden passages. They wore their robes of black and white, but as they took their seats each man pulled his cowl down to show the face he had chosen to wear that day. Their tall chairs were carved of ebony and weirwood, like the doors of the temple above. The ebon chairs had weirwood faces on their backs, the weirwood chairs faces of carved ebony.
—A Dance with Dragons
This group has some overlap with those Arya has seen before:
After three hours of wine and words, the priests took their leave … all but the kindly man, the waif, and the one whose face bore the marks of plague.
—A Dance with Dragons
The text seems to indicate that Arya is not counting herself in this number, so that makes a dozen Faceless Men. We at least know that there are significantly more than two Faceless Men.
Other possible or definite Faceless Men have appeared in the books. Samwell Tarly, for instance, met "Pate" after the real Pate had died, and thus "Pate" was probably a Faceless Man.
“My thanks.” There was something about the pale, soft youth that he misliked, but he did not want to seem discourteous, so he added, “My name’s not Slayer, truly. I’m Sam. Samwell Tarly.”
“I’m Pate,” the other said, “like the pig boy.”
—A Feast for Crows
However, given that eleven is the maximum number of Faceless Men ever mentioned to be in one place at the same time, we cannot assume that there are more based on other individuals seen in the books, given the well-known propensity of the Faceless Men for disguise.
It's also worth noting that the previous passage suggests that the Faceless Men are not much more numerous, since eleven is the most Arya has ever seen together.
In the TV series Game of Thrones, we know of three Faceless Men:
Given that the Waif and Jaqen appear at the same time, we know they are different people. We can also assume that neither of them is Arya Stark, making three.
As was mentioned, there were 11 at the gathering, which I don't believe included the waif, so that's a dozen. However, I think it would be safe and wise to assume that surely there were other faceless men of unknown numbers throughout the world on current 'missions', no? It seemed that the ones at the meeting were sort of heads of the operation, not the entire organization. It seems to me that no number will ever be substantiated as the mystery only serves to add to the mystique of the order. Large numbers of excellently-trained assassins who don't fail? A force to be reckoned with surely. A small number of said assassins? A very exclusive guild, indeed, and one whose services will not be cheap. (Also, regarding a previous answer, Arya Stark would NOT make three since she was not technically yet a faceless man. She was sort of on probationary terms, I think.)