The story is Four in One by Damon Knight.
It was included in this Gollancz anthology, but this only contains stories by Damon Knight so it doesn't have any stories by Joanna Russ. I think it's a really good story and classic SF of the period. I heartily recommend forum members seek it out.
I think your Joanna Russ reference is a red herring, because I think it comes from her novel The Female Man. In chapter 9 of that book there is:
One approaches the house from the side, where it looks almost flat on its central column— only a little convex, really—it doesn't squat down for you on chicken legs like Baba Yaga's hut, but lets down from above a great, coiling, metal-mesh road like a tongue (or so it
seems; in reality it's only a winding staircase). Inside you find yourself a corridor away from the main room; no use wasting heat.
Davy was there. The most beautiful man in the world. Our approach had given him time to make drinks for us—which the J's took from his tray, staring at him but he wasn't embarrassed—curled up most unwaiterlike at my feet with his hands around his knees and proceeded to laugh at the right places in the conversation (he takes his cues from my face).
So it wouldn't have been in an anthology.