Our license agreement requires you to have enough licenses to cover every unique person with a login on any of your installations. For example, if instance A has users Bob, Shirley and Meghan, and instance B has Bob, Frank and Charlie, you need 5 licenses total (since Bob is the same person on both instances).
That said, I think it's worth looking in detail at your particular workflows to see if this is really the best setup for your needs. Separate instances would limit the ability to connect pieces of data, such as an incoming support email case which is related to a bug or feature case. If you would like some help with your options, please contact us directly.
It is technically possible to install two instances of FogBugz on the same machine in a Linux or Windows environment (this cannot be done on a Mac). This is fairly straight-forward on Windows: Simply run the installer again and tell it to install into another directory, and you'll have a second installation. Only a single Maintenance Service should run, however.
In a Linux environment, do the same thing, except there are some additional steps:
1) You'll need to add differentiating symlinks in the init.d directory; normally one links to the fogbugz/bin/fogbugzctl script and is called (appropriately) 'fogbugzctl'. You'll need to make a new link to the new script.
2) You'll need to decide how you want the websites to be organized (what hostname/path should you use to reach each one?) and set that up manually in Apache.
Multiple heartbeat processes will run on Linux, which is fine.
If you need technical assistance with any of that, I suggest you first strongly consider whether or not you really need to do this. Afterward, you can contact us for help.