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Feel free to add more details. How are you sharing the vault?
If this is about Obsidian Sync, please mention that.
And what do you mean by “active at the same time”? I guess I don’t know Linux, but in Mac and Windows you can have multiple vaults open at the same time.
But are you referring to nested vaults? If so, it’s already an open request, and some people have had success with doing it, as far as I know. Nested Vaults (vault within a vault)
But then why would you need to mount the other vault inside your personal vault to be able to share it with people? (I’m not questioning your motives. Simply asking for more details, so it’s easier for people to help or offer workarounds.)