When you enable multifactor authentication in Microsoft 365 (formerly Office 365) with an existing tenant, Outlook starts asking for a password and will not accept your current Microsoft 365 password. You then need to use app passwords for Outlook, rather than standard MFA with your password and a second option such as the Microsoft Authentication app, Txt, E-mail, or call. Those options work fine with access to Web and other Office Apps but not Outlook. See the following link to manage App Passwords; https://docs.microsoft.com/en-us/azure/active-directory/user-help/multi-factor-authentication-end-user-app-passwords#:~:text=To%20create%20app%20passwords%20using%20the%20Office%20365,password%2C%20and%20then%20select%20Next.%20More%20items…%20
You can however enable standard MFA methods for Outlook using powershell. The credit for most of the instructions below goes to; https://www.petri.com/enable-modern-authentication-exchange-online
Instructions to enable MFA with Exchange On-line (paraphrased)
When asked for credentials, you need to use an O365 admin account that does not have MFA enabled. I create one without an Office license just for this.
I use the PowerShell ISE but I suspect standard PowerShell run as admin will work as well
Connect to an Exchange PowerShell session by running the following 2 lines
$UserCredential = Get-Credential
$Session = New-PSSession -ConfigurationName Microsoft.Exchange -ConnectionUri https://outlook.office365.com/powershell-liveid/ -Credential $UserCredential -Authentication Basic -AllowRedirection
This is not in the Petri link above, but you need to run the following line to allow running scripts
Set-ExecutionPolicy RemoteSigned
Test if MFA is already enabled. Will return “false” if not enabled
Get-OrganizationConfig | ft name, *OAuth*
Assuming not enabled run
Set-OrganizationConfig -OAuth2ClientProfileEnabled:$true
Then run the following again to confirm now enabled, i.e. “True”
Get-OrganizationConfig | ft name, *OAuth*
Close session
Remove-PSSession $Session
I find it takes 30-60 minutes before the policy is applied and changes in use