You can definitely do that. Three options:
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One Auth0 Tenant per Customer: Each customer gets their own tenant, completely separating all data and code. Advantages: clear separation between customers, customized tenant configuration per customer. Disadvantages: Maintaining multiple tenants!
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Single Tenant, with One User Database per Customer: Each customer gets their own user database, but in a single shared tenant. Advantages: probably easier for you to maintain, possibly opportunity to share code between customers, user data still separated. Disadvantages: less flexibility at the tenant configuration level.
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Single tenant, single database: This is probably not a good solution, unless the customer data should be shared between customers. You could use a single database but including data in the user profiles that allows you to differentiate users by customer. Then your app could handle what data each customer can see. This model has the greatest risk of a data exposure.
In either case above, each deployment of your software would have its own Application (Client) in the Auth0 dashboard, and therefore its own unique set of client credentials. Authorized scopes can be adjusted for each deployment of your application as appropriate for that deployment.