Sure, you would just override the get() and post() and possibly dispatch() methods in your classes as needed.
I always recommend the classy CBV inspector, helps immensely with understanding the available methods and inheritance in the CBV's.
Also check out the source code of Django to see how they implement each of the generic CBV's on GitHub in django.views.generic.
However, if you have working view functions, what is the"need" to switch to CBV's?
FBV's may be more appropriate if you have a ton of logic to handle various types of requests via a single view, which sounds like it may be the case here. CBV'S don't pay out well in that regard from a simplicity standpoint, although they are more than capable.
-James