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There’s a limit to the amount of devices you can register for the Intune Company Portal app.
To fix this, yes you’ll need to remove a device attached to your account. This is not done via Outlook for Web, where you can remove devices – that’s purely for Outlook. It’s also not done via https://myaccount.microsoft.com/device-list as it’s not removing it from Azure.
As per Microsoft Documentation , there’s Intune device limits, and Azure device limits. Intune / EndPoint Manager has a maximum of 15 devices, where Azure has a default of 20, but can be changed to a few different values, including ‘unlimited’.
To remove devices from a user, and admin should use Azure Active Directory and go to Users > Find the user > then under Manage, choose ‘Devices’. Any old device (check by the activity date) can be selected and deleted.
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After removing enough devices here, you should be able to register the new device via the Intune Company Portal app again – and in my testing, this was next to instant.