It is required to add a custom domain to Office 365 to federate your Office 365 tenant with Advanced Authentication as the external identity provider. You cannot federate your onmicrosoft.com domain. It is not recommended to set the custom domain that you have added to Office 365 as the default domain. However, if you set the custom domain as default then you cannot federate it.
To enable single sign-on to Office 365 perform the following tasks: