If the original work is itself a satire, do you try to make a humorless version of it?

Hmm...

"In the seminal Zucker, Zucker, and Abrams opus Airplane!, one character, played by Leslie Nielsen, asks another to pilot an passenger airliner in an emergency. The would-be pilot responds with incredulity, but is coolly rebuffed by the Leslie Nielsen character. This evinces laughter from the audience, as the exchange involves a confusion between two near-homophones."

Heh, heh... still funny.

For less goofy, more drily satirical stuff, I think that making a satire of the satire is still a viable option.