Is that possible to single sign-on with completely different domains?
Have you tried the Domain module? I've looked into it a bit, and seems to do what you need (though I myself have not set up my site yet with it, so I'm not positive). According to the documentation:


  The module allows you to share users, content, and configurations across a group of sites such as:
  
  
  example.com
  one.example.com
  two.example.com
  my.example.com
  thisexample.com &lt;-- can use any domain string
  example.com:3000 &lt;-- treats non-standard ports as unique
  


https://www.drupal.org/project/domain