An active plan should be allowed to be modified in many ways:
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Change of the name of the plan (already mentioned elsewhere)
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Anything that further restricts the plan should be allowed. Example include: adding random letters to type, changing a plan from random letters to forced mode, or making any schedule tighter, or allowing the plan to be restarted automatically the next day, or extending a plan with a certain end, etc.
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It should be possible to fully view the plan, even when active. Right now if I want to understand an active plan, I have to clone it, just to view it.
Finally, to avoid errors, make sure the user confirm the changes.