Since last we left them there would be only two who were both Hunters of Hircie and the Warriors of Ysgrammor's Legacy - You (if you remained True to the Bloodmoon) and Aela. If you, the player, did decide to abandon the Pure Hunter that is the Werewolf; then she'd be all that is left.
the question is - would the Companions still function as both? While considering that th Companions first became Werewolfes after making a deal with the Witches of Glenmoril, and just managed to go with that. Only making sure that the Circle, the High Elite Captains of the Companions, would be granted the Blessing of the Hunt / Curse of the Prince. And for the most part, it seems to work out for them. The only detail that seems to agitate them is the fact Sovrngarde can not be obtained if you are a Werewolf. You simply go to the Hunting Grounds, and Hunt. So, there doesn't seem to be a moral dispute or even a mechanical dispute over it. They did, indeed, become greater Hunters and Warriors. The witches didn't lie, and Kodlack's only frustration was the tidbit over afterlife.
So, who is to say the Companions would not embrace Lycanthropy if they did not care for Sovrngarde? Which is mostly a Nordic belief and Nordic core ideology, that is the highest place of honor and the place to go. Sovrngarde. Yet to, say, a Dunmer or Khajit or Imperial - what is Sovrngarde? Some Afterlife for the Nords, excluding Ysgrammor who was Amoran.
And since there /is/ a presence of Dunmer and Imperial in the Companions, doesn't seem too odd that one may eventually become apart of the Circle. Hell a High Elf became Harbringer.
Though, with only one left, is it really possible? Or is this only a weak-story telling device as well as the only way (in vanilla) to introduce the werewolves?
Soon to be discarded and left to the rubble.