Troubles with Clean URLs enabled

Seem to be having troubles with Shared Sign-On and Clean URLs enabled, and I'm hoping that I've just done something silly.

To ensure no potential interference from other modules, I've installed a clean 5.7 test site.

Two domains:
- www.mysite.com
- www.othersite.com/blah

Single shared database for both sites - i.e. both sites are exactly the same.

Master URL: http://www.mysite.com

- sites/default/settings.php for www.mysite.com
- sites/www.othersite.com.blah/settings.php for www.othersite.com/blah

Both settings.php files are exactly the same.

With Clean URLs disabled, am able to switch between domains with no issues (logged in or not).

With Clean URLs enabled, cannot cleanly switch URLs regardless of logged in state.

Steps:

1) Clear browser cache and cookies.

2) Go to www.mysite.com

3) Manually type in www.othersite.com/blah

4) Result: redirect "back" to master URL with a "Page not found"

Final URL: http://www.mysite.com/blah/singlesignon/initial_check?slave_session=khct...

In my mind, www.mysite.com at the beginning of the final URL should actually be www.othersite.com?

SUE on my part in the configuration?

Cheers,

Andrew