IMHO you are taking a bad approach at the problem.
Users are unique, and should be unique for the application “sanity”.
If you think at your site structure, you have users that can registrer to courses. You want to have unique “entries” for every course, and that’s legit, but to do that, you should not duplicate users, but create an intermediary “entity” that as a one-to-many relation with users and one-to-many relation to courses.
In WordPress, when you need a generic “entity”, solution is, mostly, register a new post type.
Let’s assume you register a post type called “registration”.
Now you can connect users to registration using post_author field, in this way every user can have multiple registrations and every registration belong to one user.
Probably, registration can have some meta fields, e.g. one can be ‘Pupil Name’, where in case of user is a parent registering a child, is filled whit child name, in case user is an adult that want to apply to more courses pupils name is jsut user name.
Now you have the problem to connect this new post type to courses (that probably are another CPT).
WordPress has a lack here, because out-of-the-box is not possible connect posts to other posts, but you can solve the problem using a plugin like Posts2Posts ore create relationship by yourself using a custom field (something like a '_course_id' custom field for registration post type).
That’s the structure: you have unique users with unique emails, usernames and passwords.
Every user can login, manage the profile, get a new password when forgot, and any other feature a user should have.
At same time users can have multiple registrations, one for every courses.
In this way you can know how many pupils you have per course using a simple meta_query: ‘registration’ post type where meta_key = ‘_course_id’ and meta_value = $a_course_id.
Creating this structure is relatively easy, what you have to write is the UI to create new registration.
If users should not have possibility to register themself, you can use the core post type creation page:
create new registration post -> set post author to the wanted user -> use a metabox to select the related course.
Otherwise, if you want users are able to create new registration, you have to make registration post type non-public (hiding default UI) and create a custom UI for the purpose.
It’s a bit of work, but your application will improve a lot, structure will be “sane”, and you will be able to easily expand the site features, e.g. using newletter plugin to contact users (without worries about duplicate emails), integrating some shopping cart plugin to allow online pay for registrations, and so on.