Now, I know I said I'm not trying to be high-brow here, but I feel compelled to reference Moliere. You've been warned.
In "L'Impromptu de Versailles" (The Rehearsal at Versailles, also translated as A Versailles Improvisation), Moliere takes his critics head on in a most unusual manner. His critics had done this exact sort of thing we're talking about now, namely, trying to parody his works, which were comedies (and very sharp comedies, too).
Moliere's response was to tell them that they could never hope to write anything as funny as his stuff, that any humor in their stuff would be directly plagiarized from his plays, that nothing they could do could rile him up or get him mad, and he was just going to go ahead writing great plays and making more money than them - but because he was Moliere, he did it all in a play.
"L'Impromptu de Versailles" states all of the above very directly, but puts it all in the context of Moliere and his troupe in a last-minute rush to prepare a play for the king. He paints himself as frustrated and somewhat ineffectual and all his troupe as less than competent, and still manages to find time to make fun of the stupid things other theater companies did when they were trying to be serious and when they were trying to parody comedy, especially Moliere's comedy (we acted this out in 12th-grade drama class and had a marvelous time).
The play's not perfect, but it's still funny and still relevant, and Moliere's remarks on the futility of parodying comedy are quite relevant (some of the play can be read here [http://books.google.com/books?id=PBBRJssSobkC&pg=PA95&dq=rehearsal+at+versailles&ei=YbwZS5TZFKOykAT1pOXcCw#v=onepage&q=rehearsal%20at%20versailles&f=false], and if you read French you can get the whole thing here [http://www.site-moliere.com/pieces/imprompt.htm]).
Rather than parody a parody (or worse, parody a parody of a parody), Moliere parodies the people dumb enough to try to do so, and makes fun of himself while he's at it to give the piece some more depth. That's how it's done, and that's why we fondly remember Moliere 300 years later while we're doing our best to forget "Meet the Spartans".