"Sorry, another account from your organization is already signed in on this computer" when signing into Microsoft 365

Issue
When signing in to an Microsoft 365 desktop app (such as Word or Excel) using your Microsoft 365 user ID and password, you receive the error message:

"Sorry, another account from your organization is already signed in on this computer."

Cause
This is expected behaviour. It occurs if you are trying to sign in using an Microsoft 365 account that is from the same organization as the Microsoft 365 account that is already logged in on your Computer or Office Desktop app.

Solution

1. Sign out of the accounts (for the same domain) that are signed in.
2. Then restart that computer.
3. Sign back in to the Microsoft 365 application, but this time, click on "This App only", so that your computer doesn't save your login and therefore it doesn't use it for other applications that use a Microsoft 365 account.
4. You should also unselect "Allow my organization to manage my device". Selecting this will cause issues moving forward, as it will prohibit you from choosing a specific Microsoft 365 login to be used for each Office application, which in turn stacks your Microsoft 365 logins, causing the above error. However, when This app only is selected, that should bypass the setting for "Allow my organization to manage my device".
   
    

If this does not solve the issue, try the workaround below.

Workaround

Step 1 - Remove Microsoft 365 profiles and log in again.

In this example, user ronald.silvosa@fyidocs.com is already logged in, but you are trying to login as user troy.steele@fyidocs.com.

1. In the top right-hand corner of a Microsoft 365 app (Word, Excel), select your name, and then select Switch Account.

2. On the Accounts screen, click Sign out.

   

3. Click the account with the same domain name that you want to remove, and then click Sign out.

Step 2 - Remove connected services from your Microsoft 365 profile

1. Go to File, and then click Account.

2. Click on either Sign out or Switch account.

   

Step 3 - Clear cached credentials on the computer

Remove the cached credentials in Credentials Manager:

1. Select Start, then Windows System, then open the Control Panel and select Credential Manager.

   Note: You may have to use the search field in the Control Panel to find the Credential Manager.

2. Under the Windows Credentials tab, locate the account that you want to remove and then click Remove.
   
   Note: In Windows 7, this is listed as Generic Credentials.

   

3.  Log off, and then log back in to the computer.

More information
In Microsoft 365 apps, you can access Microsoft 365 content in SharePoint Online by providing your Microsoft 365 user ID and password. If you have multiple Microsoft 365 user IDs from different organizations, you can access content from the SharePoint Online deployments of each organization.

However, Microsoft 365 only supports one Microsoft 365 user sign-in from each tenant or organization per session.

Microsoft 365 makes a best effort to prevent a second user from signing in when another user from the same organization is already signed in. However, there may be cases in which this scenario is not detected and the Microsoft 365 user interface may show that another user is successfully signed in. In this case, the second user cannot access his or her own content. All Microsoft 365 content that a user tries to open will be performed by using the first user’s credentials.

Be aware that Microsoft 365 respects the permissions of all documents and SharePoint Online libraries. That is, if the first user doesn’t have access to a document that the second user has access to, and the second user (who believes they are signed in) attempts to open that document, the document will not open because Office tries to open the document as the first user.

To fix this scenario, the signed-in user should sign out of Microsoft 365, and then restart his or her computer. Doing this makes sure that a clean state is present when the other user tries to sign in again.

If the above workaround(s) does not resolve the issue, then adjusting the registry is the final solution.

References:
https://docs.microsoft.com/en-us/office/troubleshoot/error-messages/another-account-already-signed-in