Hi @Aoge
Microsoft Teams Premium Planner should have the same features as the basic version, including copying and moving tasks.
1). Please make sure your Planner app is the latest version. Maybe older versions of the app are missing some features or have bugs.
2). Please try clearing the cache of the Teams app or try logging into Teams on a different device or browser to see if the problem persists.
If you want to know which features are supported by both Basic and Premium plans, and some features are only available on specific plans, please refer to this reference.
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