login across multiple domains

Background
I have a customized theme (from another company) that is streamlined and very well fitted for a specific task. However, i have some more functions beyond this theme's focus that I need. To avoid cluttering this theme, i was thinking of having the menu go to another domain (via permalink) to handle a new set of menus. And i was thinking of using your business theme to anchor these menus.

Question
Can the log in be shared and synchronized automatically across themes, so the end user does not notice? If yes, then how?

thanks,
Mark