Custom comparison functions for built-in types in Python

I am using Python's built-in sets to hold objects of a class I have defined. For this class, I defined __eq__, __ne__, and __hash__ so that I can compare objects by my custom comparison functions. That works just fine, until I find out that I actually need two sets of comparison functions, which will be used in different ways at different times in my code.

I can't define two sets of __eq__, etc. methods in my class, and Python's built-in set type does not accept a comparator argument. I suppose I could go write a wrapper class around set, but that seems like a lot more work than necessary.

Is there any easier solution to this than writing my own set class?