I am not trying to change my e-mail in the various StackExchange profiles I have.
Rather, when I log into a StackExchange site, and I log in using the StackExchange OpenID, I use my e-mail. I want to change that e-mail. Is it possible?
When I get to my StackExchange profile and I click on the "Logins" link, I get an option to add more logins, but not to edit the one I already have there.