add function in user page

Hello, I already posted a project like this but was not cleared enough so I deleted. So, I have a very simple project : Currently wordpress to add an user, has 2 forms : one if you are already member of a subsite, and another form is you are a new user (see picture [login to view URL]) So, project is to merge these 2 forms in just 1 and place the form in "user page" like picture [login to view URL] username form (in register new user see picture [login to view URL]) must not be displayed and must be replaced by the email. admin must not receive message error or anything. Everything must be transparent for him and the plugin has to work behind and see if user already register or not and adjust in case. Thank you