Doing a quick search here not sure it would or could be done too easily.
A maybe easier route might be use a toggle tied to primary group and have 2 groups that switching from group A to group B switches Theme’s and maybe uses something like the Theme component Custom Home page for groups? Or perhaps uses Modern Category+group boxes installed twice(used in air theme) with customizations based on theme/primary group
While I don’t know myself. I would wonder if having 2 discourse installs might risk corrupting the database? Though some have staging sites, but I think the staging site is backed up off the main one routinely?