I know about the __add__ method to override plus, but when I use that to override +=, I end up with one of two problems:
(1) if __add__ mutates self, then 
z = x + y
will mutate x when I don't really want x to be mutated there.
(2) if __add__ returns a new object, then
tmp = z
z += x
z += y
tmp += w
return z
will return something without w since z and tmp point to different objects after z += x is executed.
I can make some sort of .append() method, but I'd prefer to overload += if it is possible.