What would monks do?
I'm not being flippant: I would use Catalyst. One of its great strengths is flexibility in deployment. You can have as many copies of an app running side-by-side under different web/app-roots as you like if you set it up right; all setting it up right means is you use uri_for() to construct URIs in templates so they move with the app's context, and you change your underlying config file (and possibly the engine/server) for each. You're only limited by the RAM you've got v what each copy needs (averages I've seen are 80-150MB).