If a customer is already activated they can't then use another product key to activate the very same app. They either have to deactivate, and then use the new key, or you would need to re-evalute why you're giving customers multiple product keys for an app on a computer.
If it's for subscriptions or renewals, we have a method for that: custom license fields: https://wyday.com/limelm/help/license-features/
With custom license fields a customer can use their single product key and you can update their expiration date (either manually or as part of an automated process).