Registering a Teradek

Can a teradek be registered by 2 different stakes? (Background: I have a ward that belongs to another Stake in attending our building and they want to use the teradek, can it be registered on their Stake webcast portal without affecting our use of it?)

I've done this when the feature first came out, but each stake would get a different Remote Configuration URL that has to be set on the Teradek for it to pull done the configuration which sort of defeats the purpose.

For me, I found it easier for sacramemt meetings to keep it registered under the Stake that has more wards and coordinated with the other Stake Tech Specialist to setup the 3rd wards sacramemt meeting.
I only change the remote config url to the other stake for a stake conference and change it back after.