Best way for multi tenancy with shared users

Hi All. Looking for best way to achieve the following:

Current Scenario:
Single Auth0 Tenant.
1x React Application using Client Credentials Flow
1x API, using Roles and Permissions.

So far, client logs into application, the Access Token is issued for the API audience and augmented with the Role.

Future State:
1 x Client Application
1 x API
However internally to the application/api there are two “tenants” - Say one for Business A and one for Business B. The API should return data tagged in the database based on which “Business” is selected.
Users could be on either business, or both businesses, so a drop down to “change” business if applicable to them, but still a single application and single API.

I’ve been reading that all applications in a single tenant share users, and then if I have multiple tenants, I would need a way to sync the users that need syncing, but then I don’t know how to achieve being able to “swap” businesses without having a different app and login again.

Is this something that shuold be handled on the Auth0 side, or is this something I should add an extra claim on the users profiles / tokens and just handle internally on the API?