Right now is this thing with claiming summoning contracts and the sage mode. Essentially due to the snake contract Kayenta and Zanto are, in essence, claiming snake sage mode as their own even if that wasn't their intent.
If they control the snakes then they control the sage mode that comes from the snakes. They get to do whatever they want with it. They can put the cave where they want, they can choose who they want to give it to, ect.
Say I make a contract with the great brown cow sage. Okay now I'm going to claim a contract that ties all cows to me. I place this cave in Otogakure and in order to use cows you now need to consult with me. Even if I let you sign it you cannot become a cow sage until you consult with me and I take you there. (I own cow sage mode due to this)
Also I'm totes claiming slugs to show you all how it is.(On Shadow) Shikkotsu Forest is now located in the boundaries of Otogakure.
In all technicality, if you do make a Cow contract and Sage Mode, then you
can do whatever you want with it's legendary location and summons overall, since cows aren't a canon summon or canon Sage Mode in the series.
But Slugs on the other hand are a canon summon, and perhaps have a canon Sage Mode as well. This is implied to be Hashirama's Sage Mode since he doesn't seem to have any Toad or Snake-like characteristics, and the only other place that is implied that it can be learned from is the Shikkotsu Forest.
Now let's say if you claimed Hawks or Crows, which are canon summons without a canon Sage Mode or canon legendary location, then you can go ahead and make up whatever you want for their Sage Modes and legendary location. This is what Xia has done for Hawks already though, so nobody else can really have a say on that now. Crows, I haven't done any research on who has established what on that. But these are some examples to draw from.