Wait...I've seen two ways for services to handle multiple users from a client using the same account.
1. A company using the service gets a single user login for their account. That login is shared by all of the employees who use the service.
2. A company using the service starts out with a single user login for the account. That login is meant to only be used to administer the account. The administrator can create more user logins for the account, usually with reduced privileges. Each employee is given a separate login of their own, with just the privileges needed to do their job.
I don't think I've seen a #1 that uses 2FA. I assumed that was because it could then easily run into the problem you describe.
With #2 there is no problem using 2FA, or with each user using their own device for 2FA. The only account you have make sure won't be lost if someone gets hit by a bus is the administrator account.
Did you run into a service using approach #1 but that used SMS OTP?