Microsoft 365 features that help users manage their subscriptions, account settings, and billing information.
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The Purdue work/school account and personal Microsoft account are separate identities that happen to use the same Purdue.edu address. They cannot be disconnected by merging the personal account into the existing Outlook.com account, and two personal Microsoft accounts cannot be combined.
Here are some suggestions you can try:
Sign in at https://account.live.com/names/Manage using the Purdue.edu address, then choose Personal account if prompted.
Add a new Outlook.com alias and make it primary. Do not enter the existing Outlook.com address, because it already belongs to another Microsoft account, which explains the error.
After confirming that the new alias works, remove the Purdue.edu alias from the personal account. This changes only the sign-in name, so the Microsoft 365 Family subscription, OneDrive data, and existing sharing with your wife remain with that personal account.
Keep the existing Outlook.com account separate.
If you specifically want the subscription owned by the existing Outlook.com account, it cannot be transferred. Turn off recurring billing, allow the current subscription to expire, then purchase a new Family subscription through the Outlook.com account and invite your wife again.
Thank you for your patience in reading, I hope this information has been helpful to you.
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