Short answer:
One per turn.
Explanation:
For reference, this is the original text of An Untimely Brood:
Given that each of your companies has its own site phase, some confusion arises due to An Untimely Brood’s use of “each of your site phases.” There was also confusion expressed during the 2019 ARV as to whether this effect was limited in the first place, given that it doesn’t use the word “only”.Playable if you are Radagast or Alatar and have 6 or more stage points and a protected Wizardhaven. One non-unique ally with a mind of 1 is playable at one of your tapped or untapped protected Wizardhavens each of your site phases. Cannot be duplicated by a given player.
It is this committee’s opinion that, while the wording is admittedly not as clear as it could be, ICE’s intentions with the card were clear: “one” ally may be played at “one” Wizardhaven, and once this “one” ally is played during a site phase, the effect doesn’t allow for additional allies to be played during the same turn. In the interest of clarifying how this card actually works, we are issuing the following errata:
Replace “each of your site phases” with “during any of your site phases but only once each turn”.
Although there has been some discussion as to the difference between “is playable” and “may be played” in this card's text, this committee has found that other cards beyond the scope of this digest (such as Saruman’s Machinery) similarly use the “is playable” text, so we shall revisit clarifying that distinction if necessary at a later date.Playable if you are Radagast or Alatar and have 6 or more stage points and a protected Wizardhaven. One non-unique ally with a mind of 1 is playable at one of your tapped or untapped protected Wizardhavens during any of your site phases but only once each turn. Cannot be duplicated by a given player.