User Signup in Multisite – Need Plugin or Advice

Test if the current visitor is logged in and registered as user

// If the user's not registered & logged in, abort
if ( ! is_user_logged_in() )
    return;

Test if the currently logged in user has a capability for the specific blog

$blog_id = ''; // You need to retrieve and set that here
// If the currently logged in user hasn't got the 'manage_options' cap - which is assigned to admins and above - abort
if ( ! current_user_can_for_blog( $blog_id, 'manage_options' ) )
    return;

If it’s not necessary to check for a specific blog, we can test just the capability.

// If the currently logged in user hasn't got the 'manage_options' cap - which is assigned to admins and above - abort
if ( ! current_user_can( 'manage_options' ) )
    return;

This (old and not maintained) plugin gives you better in-depth look at what users deliver.