To what extent is it possible to satirize satire, to mock at mockery?

I remember reading a parody of Gilbert and Sullivan operettas written by A.P. Herbert once and not liking it very much. It’s not that I like Gilbert and Sullivan so much that I can’t abide any mockery of them (I don’t think) but somehow it just seemed… hollow. Because it was mocking the conventions of Gilbert and Sullivan operettas, which are themselves mocking conventions of other plays. It seemed to me to be one level of mockery too far. You can make fun of something “serious”,–i.e. the conventions of stage tragedy–but you can’t make fun of something making fun of something serious.*

And it’s not just this, but I’ve run across things now and then that try to make fun of something that is making fun of something else, and it rarely seems to work. Like when MAD magazine would do a parody of a comedy film or program, it just felt weak to me, even if it was not an especially funny comedy. Whereas, when they parody a serious, or at least non-comic, film, it was usually pretty good. (I haven’t read MAD in years, however, so I can’t point to recent examples.)

What do you think?

*This raises the question: can you make fun of something making fun of something making fun of something  serious? I don’t know, but I expect it takes calculus to find the answer.