In theory it should be possible to do this, as the "container" for the discussions is a variable ("discussions" by default). This relates to the space in the Repository where the discussion objects are stored.
You'd need to duplicate the Discussion components configuration in site-data and set them to use a new container. Then do the same for the Discussions page and point it to use those components instead. Note this is all theoretical as (as far as I'm aware) this hasn't been tested particularly well, if at all.
Thanks,
Mike