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The enhancement here would be to add a fourth option type: Open Managed. The conditions for this group are that students are free to join or leave, but creation of teams is restricted to course staff only.
Technical approach[needs a technical discovery]
The necessary changes have been explored in the following PRs:
Changes in the backend:https://github.com/openedx/edx-platform/pull/33672
Register the new open_managed team.
Count the open_managed teams as part of the public teams.
Update the API to register open_managed as a valid team type.
Separate the Instructor Managed Team logic from the Can Join Team logic.
Changes to the frontend: https://github.com/openedx/frontend-app-course-authoring/pull/669
Register the new open managed type and add text descriptions.