This is possible. Even as a user of the Shared Host, you are the administrator of your website.
I am in the process of engineering a custom signup form with the API, then will start writing an App for my desktop, account admin and the likes.
The problem with the API is the documentation really sucks and it's fairly difficult to implement. Though, if you can program, you should be able to get it going with a little trial and error.
If there is great interest, well, maybe I could make a career out of it. Get out of the way Micro$oft....