Selective caching - by user Is it even possible to do this?

The goal is to group our visitors:

Group A sees Theme A
Group B sees Theme B


I am able to achieve this goal through cookies. But when caching is enabled (i.e. Site config > Performance > On), things are messed up. This is what happens:

1) Group A visits Page-1
-- Page-1 is not cached yet.
-- Cookies are properly checked.
-- Page-1 is displayed using Theme A


2) Group B visits Page-2
-- Page-2 is not yet cached.
-- Cookies are properly checked.
-- Page-2 is displayed using Theme B


3) Group A visits Page-2
-- Page-2 is already cached.
-- Cookies are ignored
-- Page-2 is displayed using Theme B (when it should be displayed using Theme A)

So now what I am thinking is, instead of using cookies, I'll use separate cache for each group.

Is this even possible? :S If not, any recommendations are welcome.

Inputs will be highly appreciated. Thanks!
Checkout Cache page based on cookie value and URL

Long story short what you want can be done. Depends on how you want to do it :)