How to avoid nested arraylike if statements in python

I often find myself coding structures similar to the following:

if x:
    if y:
        #Do thing 0
    else:
        #Do thing 1
else:
    if y:
        #Do thing 2
    else:
        #Do thing 3

Sometimes with more levels of nesting, or 3 conditions per variable, etc. I'd like to. clean up the code, so as to not repeat if y:. I've thought of creating an array of functions thing1, thing2 so on, and then indexing with f[x, y], however there is often quite different behaviour, which makes this hard. For example, in a class, thing1 might use two variables and modify another 2, while thing2 might do something entirely different with different variables (this makes returning the results in a uniform way hard).