If you're using the new "no-self" format, this shouldn't be too hard.
Let's call the first app appcopy1. In this app, make sure each page has template_name set explicitly:
class MyPage(Page):
template_name = 'appcopy1/MyPage.html'
Then, appcopy2 can just import everything from appcopy1. However, you need to copy/paste the Player/Group/Subsession class and any fields from the first app. Also you need a different name_in_url. That means your __init__.py can just be this:
from appcopy1 import *
class Constants(Constants):
name_in_url = 'appcopy2'
class Subsession(BaseSubsession):
pass
class Group(BaseGroup):
pass
class Player(BasePlayer):
xyz = models.IntegerField()
And that's it. You don't need any templates in this app, so it will just be an __init__.py with the above content and nothing else.
I haven't tested it thoroughly but in principle it should work.