I thought I read a blog post but when I tried it on Startups.com it just keeps logging me out as one user and back in as the other.
Is this allowed? And is it something StackExchange sites can turn on/off?
If you registered the two openids seperately, you'll need to contact team@stackoverflow to have them merged, unless this is a stackexchange site. There you will need to find out who the site administrators are and ask them to merge the accounts.
I don't believe there's a way for you to easily add an openid to an account if the id you are trying to add already exists in the system with another account. There may be a way if you disassociate the ID with the existing account and then re-add it, but I don't know whether the system will accept that attempt.