Can anyone share any experiences / examples where they have implemented External Identity with Embedded Login, AND allow single sign on to multiple SPs?  

Basically, our use case is we have Salesforce External Identity setup as the IDP and we have multiple SPs that need to share the same login/authentication. 

The flow would be to launch the portal (non-salesforce) and login using "Embedded Login" (we have this working). Then, we need the user to click on a link that redirects them to a new SP site, authenticated with the same credentials as they already had.

Similar to using the App Launcher, but without the end-user ever seeing the app launcher page.

Thanks in advance!