Is it a good idea to allow multiple users to have the same email at user registration?

At my company, some time ago come a customer's complaint, that complaint was about that a user could not be able to register because someone else registered an account with his email. I have to explain that, a customer is a company that hires services from the one where I work, and each customer can have a user's accounts for his employees and they manage his user's accounts by themselves.

So in order to make that customer happy, the management required that the user's registration were able to allow multiple user's accounts with the same email. In the beginning, I thought that it was a dumb idea but we, as the software development department have to obey the management's requests. So we make the necessary changes, to adapt the user registration and login systems to satisfy that request, but I don't have been in agreement with that requirement so far. After that a lot of bugs arose because of those changes, even today there are a lot of users with the same email and password but different usernames, I don't know if those users are actually being used.

I think that the recovery password and email change features are enough to solve that kind of problem, but I don't know, what's is your opinion about that?

BTW, I would like to know if there exists a standard, good practices, or something like that for user's registration