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More than likely you just need to compare the configuration on your local environment with the configuration on the original site, then make some adjustments to the database configuration for your local database.

It is possible to configure multiple database connections and have different models connect to different databases (or to use different database configurations for other code that requires a database connection). In these cases, the database configuration on the original server environment should contain configurations for multiple databases (or possibly for multiple accounts on the same database). You would just have to setup any additional configurations in your local environment.

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