What is the best way to manage multiple access using same user?

**Scenario:** We have a couple of Ubuntu servers, each with a single user. The user account has some specific software that bind to the host IP address and a specific port (we cannot change the port number, as it is a standard). We have multiple users, who want to use the software. For now, everyone is using the same account (over SSH), and we check if the others are using it before running it ourself, so that there is no conflict. I'm wondering what is the best way to handle this scenario? We could have multiple users, but that would still not solve the issue where the port is in-use. It would be great if there's a way to tell if someone else is using the machine, when we log in. Any ideas are appreciated, thanks!