Hi there, Nisar,
We are currently attempting to reduce our backlog of community posts to possibly help future visitors with similar questions -
If both database connection and enterprise connection are enabled for the organization, the Universal login can show them both when users log in to their respective Organizations.
To do that, please mark the option to Display Connection as a button (pic below) in the Auth0 tenant → Organizations-> your specific Organization → Connections → choose the enterprise connection ‘View details’ (three horizontal dots) and mark the option.
This will work with both Authentication Profiles: Identifier First and Identifier + Password.
The pic below shows how hot this would look with Identfier First.