It seems there is a update bug when you have more than one social connection of the same type in Auth0. I have created two linkedin social connections (linkedin (A) and linkedin-test (B)) in our Auth0 account via the Auth0 Management APIs.
This works fine and the two connections work correctly. However, when you try and update a connection via the Auth0 UI (Auth0 only shows the one of each social type), it incorrectly saves the settings to the other connection type.
IE Auth0 shows connection (A) but saves the settings to connection (B) via the UI.
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There’s only formal support for one social connection of each provider; as you already experienced the first issue you will stumble with is that Dashboard only shows one and it will also only edit one. Another thing to consider would be that you would now have two connections that can lead to multiples users with the same identifier as they both use the same algorithm to generate an identifier based on the information coming from the provider.
At this time, if you need something like that you’ll need to go fully custom and use additional custom OAuth2 connections to model your requirements. The custom connections would allow you to generate unique user identifiers and would also not impact the Dashboard. The downside would be that custom OAuth2 connection imply some degree of implementation code.