[Plugin: WP Multi Network] Sharing Cookies/Single Log-in

I just installed the WP Multi Network plug-in and am playing around with it a bit. I have my test installation of WordPress set up with Multi-Site enabled and configured to use sub-directories. I then installed the Multi Network plug-in to allow us to set up subdomains, and then use the sub-directory structure for individual blogs/sites under each subdomain.

One issue I noticed is that the cookies created by WordPress seem to be restricted to each individual sub-domain, meaning that, even though all networks share a single user-base, users have to login to each individual network.

Is there a way to share the cookies across subdomains? I understand that there’s no way to share cookies across root domains, but it would be nice if they could be at least shared across subdomains; rather than requiring users to login to each individual network.

I tried defining the COOKIE_DOMAIN constant within wp-config.php to “.example.com” (using my real domain rather than example.com) to try to get the cookies to be shared across subdomains, but that seemed to stop me from being able to login altogether (in addition to the fact that it would probably really mess things up if we ever map a root domain to one of our networks).

Any advice or help would be greatly appreciated.