A second website with shared user base and some shared forums would be . . . difficult. Possible, maybe, yes. It would be possible to set up multiple domain names pointing to the same place. It would probably be possible to set different default skins per domain name for pages, and redirects to appropriate domain names when clicking links, and so on, but that would require more work. It would probably also be possible to display forums in a different order depending on which domain you access, but that would also not be simple.
Basically, this stuff is possible but not necessarily easy. I'm certainly not volunteering to set it up until we know it's a success, if then (I have a lot of things to do, mostly not TWC-related).
A subforum would require no work at all. A totally separate forum would require some work and some money.