I have a single installation with multiple websites, I'd like to have the user be allowed to use their account on all websites, but not share a cart between them (as there will be different pricing rules / shipping options, etc..).

Is there a good way of doing this while not making the customer log in multiple times?  Right now I have it so the domains of the websites are all

{website prefix}.site.com

But if necessary, I could switch to

site.com/{site prefix}

If that's the only way to do it.