its very common to have multiple sites on one server. As Ramrajone said, its actually easy since you create a new Virtual Directory in IIS. There are two caveats I would add depending on what the other department wants to do.
They may want their ticketing system to be internet accessible and your current one might not be. If you enable access from the internet to their ticketing system, then yours is also internet accessible in a fashion even though the response headers are going to serve their ticket system. Security and all comes more into play then.
The 2nd is depending on how much the systems are used, your disk space will be consumed faster since there are two database files using space rather than one. This one really isn't such a big deal, but just something to watch out for.